├── README.md ├── Sperver_Wilson_Relevance.pdf ├── adamandy.pdf ├── adamandy.tex ├── changes ├── distict.pdf ├── distict.tex ├── hend2012_SuB-pragmatics-quantifier-scope.pdf ├── luke_synsalon.md ├── luke_synsalon.pdf ├── luke_synsalon_pres.pdf ├── mas ├── peercomments ├── JRAY-COMMENT-luke_prelim2_Draft1.pdf ├── gmp_comments.pdf ├── jr_review.pdf └── luke_prelim2_Draft1_McKayComments.pdf ├── prelim2.pdf ├── prelim2.tex ├── prepurge.tex ├── pres.pdf ├── pres.tex ├── presented.pdf ├── rob ├── showcase.rmd └── synsalon.tex /README.md: -------------------------------------------------------------------------------- 1 | # Scope Without Syntax: A Game Theoretic Approach -- Qualifying Paper 2 | 3 | This is a public gir repository for my second qualifying paper. 4 | 5 | ## Topic 6 | 7 | I argue that the different availabilities of scope interpretations across languages and constructions falls out from several pragmatic assumptions, and that formal syntax is not necessary as a tool to explain this data. 8 | 9 | I use Game Theory as a tool to explain the interactions between these pragmatic effects. 10 | 11 | ## "Licence" 12 | 13 | Cite with proper credit. 14 | 15 | Smith, Luke. 2017. Scope without Syntax: A Game Theoretic Approach. 16 | 17 | ## To-do 18 | -------------------------------------------------------------------------------- /Sperver_Wilson_Relevance.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/Sperver_Wilson_Relevance.pdf -------------------------------------------------------------------------------- /adamandy.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/adamandy.pdf -------------------------------------------------------------------------------- /adamandy.tex: -------------------------------------------------------------------------------- 1 | \documentclass[aspectratio=169]{beamer} 2 | 3 | \resetcounteronoverlays{exx} 4 | \usepackage[utf8]{inputenc} 5 | \usepackage[backend=biber, style=authoryear-icomp]{biblatex} 6 | \usepackage{tikz} 7 | \usepackage{blindtext} 8 | \usepackage{tipa} 9 | \usepackage{cgloss4e} 10 | \usepackage{gb4e} 11 | \usepackage{qtree} 12 | \usepackage{enumerate} 13 | \usepackage{longtable} 14 | \usepackage{textgreek} 15 | \usepackage{parskip} 16 | \usepackage{color} 17 | \usepackage{textcomp} 18 | \addbibresource{$HOME/Documents/LaTeX/uni.bib} 19 | 20 | \newcommand{\normalgame}{ 21 | \begin{figure} 22 | \begin{center} 23 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 24 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 25 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 26 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 27 | \begin{tikzpicture} 28 | \node {Nature} 29 | child{ 30 | node{Speaker} 31 | child{ 32 | node(d){Hearer} 33 | child{ 34 | node{$\displaystyle\binom{c}{c}$} 35 | edge from parent 36 | node[left]{$S$} 37 | } 38 | child{ 39 | node{$\displaystyle\binom{-i}{-i}$} 40 | edge from parent 41 | node[right]{$I$} 42 | } 43 | edge from parent 44 | node[left]{$A$} 45 | } 46 | child{ 47 | node(a){Hearer} 48 | child{ 49 | node{$\displaystyle\binom{-p}{0}$} 50 | edge from parent 51 | node[left]{$S$} 52 | } 53 | child{ 54 | node{$\displaystyle\binom{c-p-i}{c-i}$} 55 | edge from parent 56 | node[right]{$I$} 57 | } 58 | edge from parent 59 | node[right]{$P$} 60 | } 61 | edge from parent 62 | node[left]{${Sub}>{Obj}$} 63 | } 64 | child{ 65 | node{Speaker} 66 | child{ 67 | node(b){Hearer} 68 | child{ 69 | node{$\displaystyle\binom{0}{0}$} 70 | edge from parent 71 | node[left]{$S$} 72 | } 73 | child{ 74 | node{$\displaystyle\binom{c-i}{c-i}$} 75 | edge from parent 76 | node[right]{$I$} 77 | } 78 | edge from parent 79 | node[left]{$A$} 80 | } 81 | child{ 82 | node(c){Hearer} 83 | child{ 84 | node{$\displaystyle\binom{c-p}{c}$} 85 | edge from parent 86 | node[left]{$S$} 87 | } 88 | child{ 89 | node{$\displaystyle\binom{-p-i}{-i}$} 90 | edge from parent 91 | node[right]{$I$} 92 | } 93 | edge from parent 94 | node[right]{$P$} 95 | } 96 | edge from parent 97 | node[right]{${Obj}>{Sub}$} 98 | }; 99 | \draw [dashed](d)to[in=180](b); 100 | \draw [dashed](a)to[in=180](c); 101 | \end{tikzpicture} 102 | \end{center} 103 | \end{figure}} 104 | 105 | \newcommand{\scramblegame}{ 106 | \begin{figure} 107 | \begin{center} 108 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 109 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 110 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 111 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 112 | \begin{tikzpicture} 113 | \node {Nature} 114 | child{ 115 | node{Speaker} 116 | child{ 117 | node(d){Hearer} 118 | child{ 119 | node{$\displaystyle\binom{c}{c}$} 120 | edge from parent 121 | node[left]{$S$} 122 | } 123 | child{ 124 | node{$\displaystyle\binom{-i}{-i}$} 125 | edge from parent 126 | node[right]{$I$} 127 | } 128 | edge from parent 129 | node[left]{$A$} 130 | } 131 | child{ 132 | node(a){Hearer} 133 | child{ 134 | node{$\displaystyle\binom{0}{0}$} 135 | edge from parent 136 | node[left]{$S$} 137 | } 138 | child{ 139 | node{$\displaystyle\binom{c-i}{c-i}$} 140 | edge from parent 141 | node[right]{$I$} 142 | } 143 | edge from parent 144 | node[right]{$Sc$} 145 | } 146 | edge from parent 147 | node[left]{${Sub}>{Obj}$} 148 | } 149 | child{ 150 | node{Speaker} 151 | child{ 152 | node(b){Hearer} 153 | child{ 154 | node{$\displaystyle\binom{0}{0}$} 155 | edge from parent 156 | node[left]{$S$} 157 | } 158 | child{ 159 | node{$\displaystyle\binom{c-i}{c-i}$} 160 | edge from parent 161 | node[right]{$I$} 162 | } 163 | edge from parent 164 | node[left]{$A$} 165 | } 166 | child{ 167 | node(c){Hearer} 168 | child{ 169 | node{$\displaystyle\binom{c}{c}$} 170 | edge from parent 171 | node[left]{$S$} 172 | } 173 | child{ 174 | node{$\displaystyle\binom{-i}{-i}$} 175 | edge from parent 176 | node[right]{$I$} 177 | } 178 | edge from parent 179 | node[right]{$Sc$} 180 | } 181 | edge from parent 182 | node[right]{${Obj}>{Sub}$} 183 | }; 184 | \draw [dashed](d)to[in=180](b); 185 | \draw [dashed](a)to[in=180](c); 186 | \end{tikzpicture} 187 | \end{center} 188 | \end{figure}} 189 | 190 | 191 | \usetheme{PaloAlto} 192 | %\usecolortheme{beetle} 193 | \setbeamertemplate{headline}{} 194 | \setbeamertemplate{frametitle}[default][center] 195 | 196 | \title{Scope without Syntax} 197 | \author{Luke Smith} 198 | \date{December 1, 2017} 199 | \institute{University of Arizona} 200 | 201 | \begin{document} 202 | 203 | 204 | \begin{frame} 205 | 206 | \maketitle 207 | 208 | \end{frame} 209 | \section{Background} 210 | 211 | \begin{frame} 212 | \frametitle{Generative syntax has an poor record with scope\ldots}\pause 213 | 214 | \begin{itemize} 215 | \item Scope is often used as a metric understanding the underlying structure of a sentence (is there covert movement? phase edges? etc.)\pause 216 | \item Despite this, there's \emph{no really systematic} metric for how scope interacts with the syntax (see the literature in response to \textcite{han07}).\pause 217 | \item Scope is highly sensitive to linear order. Minimalist syntacticians either have to deny this or model it as a crazy coincidence (Antisymmetry, or see works like \textcite{collins17}).\pause 218 | \item Scope is \emph{highly} dependent on context (Chomsky's Aphasia). 219 | \end{itemize} 220 | \end{frame} 221 | 222 | \begin{frame} 223 | \frametitle{This is a social construct!} 224 | \begin{center}${\forall}x{\exists}y, eat(x,y)$\end{center}\pause 225 | \begin{itemize} 226 | \item We place quantifiers visually to the left\ldots\pause 227 | \item Corresponding visually to ``the place they take scope''.\pause 228 | \item Both of these \emph{are metaphors}.\pause 229 | \item \textbf{YET}, there's a tendency for some linguists to talk about the notation of formal logic as if it's somehow psychologically real.\pause 230 | \begin{itemize} 231 | \item We physically move quanitifers in our derivations to get the right ``logical form''.\pause 232 | \item Linguistics Wars: does formal logic create language or \textit{vice versa}? 233 | \end{itemize} 234 | \end{itemize} 235 | \end{frame} 236 | 237 | \begin{frame} 238 | \frametitle{Let's Divorce Scope from Syntax}\pause 239 | 240 | \begin{itemize} 241 | \item This is not a new theory of syntax.\pause 242 | \item But an account of scope without reference to syntactic structure.\pause 243 | \item Why?\pause 244 | \begin{itemize} 245 | \item It's Minimalist\texttrademark.\pause 246 | \item We can handle the linear order effects and the context dependence of scope. 247 | \end{itemize} 248 | \end{itemize} 249 | 250 | \end{frame} 251 | 252 | \section{English Data} 253 | 254 | \begin{frame} 255 | \frametitle{Typical Scope Data (English)}\pause 256 | 257 | \begin{itemize} 258 | \item English active sentences tend to be ambiguous:\pause 259 | \begin{exe} 260 | \ex \begin{xlist} 261 | \ex Every arrow hit a target. (${\forall}>{\exists},{\exists}>{\forall}$)\pause 262 | \ex Some jackass ruins every party. (${\forall}>{\exists},{\exists}>{\forall}$) \pause 263 | \end{xlist} 264 | \end{exe} 265 | 266 | \item But their passive equivalents tend not to be\ldots\pause 267 | \begin{exe} 268 | \ex 269 | \begin{xlist} 270 | \ex A target was hit by every arrow. (${\exists}>{\forall}$)\pause 271 | \ex Every party is ruined by some jackass. (${\forall}>{\exists}$)\pause 272 | \end{xlist} 273 | \end{exe} 274 | \item NB: There are some differences between scopes of universals and existentials. This won't be a part of my analysis, but I'll talk about it later. 275 | \end{itemize} 276 | \end{frame} 277 | 278 | \section{Model} 279 | 280 | \begin{frame} 281 | \frametitle{Intuitions of the Theory}\pause 282 | 283 | \begin{itemize} 284 | \item In the abstract, \emph{all} possible quantifier scope interpretations are possible\ldots\pause 285 | \item But, given context, the cost of communication and other pragmatic effects, we narrow down on the plausible interpretations.\pause 286 | \item Unambiguous sentences are those with one sensible interpretation left, while ambiguous ones have several.\pause 287 | \item Interesting empirical correlates, but we'll get into that later. 288 | \end{itemize} 289 | 290 | \end{frame} 291 | 292 | 293 | \begin{frame} 294 | \frametitle{Implementation: Game Theory}\pause 295 | 296 | \begin{itemize} 297 | \item I'll be using Game Theory for this analysis.\pause 298 | \item Game Theory is a way of formalizing decision-making in a \textbf{game} where \textbf{players} have the opportunity to choose among different \textbf{strategies} to achieve different \textbf{payoffs}.\pause 299 | \item E.g. a game of paper-scissors-rock:\pause 300 | \begin{itemize} 301 | \item Two players\pause 302 | \item Each player has three different strategies: paper, scissors or rock.\pause 303 | \item The winner gets a ``payoff'' to symbolize victory. 304 | \end{itemize} 305 | \end{itemize} 306 | \end{frame} 307 | 308 | \begin{frame} 309 | \frametitle{Our Game}\pause 310 | \begin{itemize} 311 | \item Three players: a Speaker, a Hearer and \emph{Nature}\pause 312 | \item Goal: the Speaker communicates the correct message to the Hearer.\pause 313 | \item Strategies (they happen in this order):\pause 314 | \begin{itemize} 315 | \item Nature has two: it (randomly) decides if the sentence the Speaker produces should have the agent scoping over the patient or \textit{vice versa}.\pause 316 | \item The Speaker, knowing what Nature has decided, decides whether to word a sentence as an \textit{Active} one or a \textit{Passive} one.\pause 317 | \item Lastly, the Hearer, ignorant of Nature's choice, but knowing what the Speaker said, chooses whether to interpret the sentence with a \textit{Surface} scope reading or an \textit{Inverse} scope reading. 318 | \end{itemize} 319 | \end{itemize} 320 | \end{frame} 321 | 322 | \begin{frame} 323 | \frametitle{Payoffs and Costs}\pause 324 | 325 | \begin{itemize} 326 | \item Both the Speaker and Hearer get a payoff of $c$ (for \textbf{c}ommunication) if the Hearer ends up figuring out the right reading from the Speaker's sentence. This is the MacGuffin.\pause 327 | \item Certain constructions, like passives are marked. The Speaker's payoff is deduced by $-p$ when he employs a passive.\pause 328 | \item Inverse scope is also non-preferred. When the Hearer reconstructs a sentence with inverse scope, both players lose $-i$. 329 | \end{itemize} 330 | \end{frame} 331 | 332 | \begin{frame} 333 | \frametitle{The Entire Game} 334 | \normalgame 335 | \end{frame} 336 | 337 | \begin{frame} 338 | \frametitle{Meta-game Thinking}\pause 339 | 340 | \begin{itemize} 341 | \item Why would the Speaker undergo the cost of passivization unless it improved his position? (i.e. to avoid the inverse scope penalty) \textit{Passivization as signalling.}\pause 342 | \item This would seem to indicate that if the Speaker has chosen \textit{Passive}, Nature has chosen $Obj > Sub$.\pause 343 | \item But if the Speaker has chosen \textit{Active}, two hypotheses are possible:\pause 344 | \begin{itemize} 345 | \item This is indeed the desired scope order.\pause 346 | \item Inverse scope is the correct interpretation, but the Speaker doesn't mind taking $-i$ because $-p$ is more grave.\pause 347 | \end{itemize} 348 | \item Result: there's only one plausible choice if the Speaker uses a Passive, but there are two possibilities if he uses an Active (ambiguity). 349 | \end{itemize} 350 | \end{frame} 351 | 352 | \section{Scrambling} 353 | 354 | \begin{frame} 355 | \frametitle{What if there's another strategy?}\pause 356 | \begin{itemize} 357 | \item Some languages have free word order, and unlike English can acheive surface scope without marked transformations/additional material.\pause 358 | \item These languages are nearly entirely scopally unambiguous and take only surface scope \parencite{karimi03}.\pause 359 | 360 | \begin{exe} 361 | \ex\label{pers} \begin{xlist} 362 | \ex {\gll Yek d\=aneshju hame ket\=ab-i x\=and. \\ 363 | a student all book-IND read \\ 364 | \trans{``A student read every book.''\hfill ($\exists > \forall$; *$\forall > \exists$)}}\pause 365 | \ex {\gll Hame ket\=ab-i yek d\=aneshju x\=and. \\ 366 | all book-IND a student read \\ 367 | \trans{``A student read every book.''\hfill ($\forall > \exists$; *$\exists > \forall$)}} 368 | \end{xlist}\end{exe} 369 | \end{itemize} 370 | \end{frame} 371 | 372 | \begin{frame} 373 | \frametitle{In other scrambling languages as well\ldots}\pause 374 | 375 | \begin{exe} 376 | \ex{\gll dass eine Frau jeden liebt\\ 377 | that a woman everybody loves\\ 378 | \trans{``\ldots that everyone loves a woman\label{g}''\hfill (some $>$ every; ??every $>$ some)}}\pause 379 | \ex{\gll dass jeden eine Frau liebt\\ 380 | that everybody a woman loves\\ 381 | \trans{``\ldots that everyone loves a woman\label{gs}'' \hfill (every $>$ some; ??some $>$ every)}} 382 | \end{exe} 383 | \end{frame} 384 | 385 | \begin{frame} 386 | \frametitle{\textit{Scramble} as an alternative strategy}\pause 387 | 388 | \begin{itemize} 389 | \item We can say that in these languages, Speakers have the additional strategy \textit{Scramble}, which achieves a different word order without the $-p$ cost.\pause 390 | \item Let's examine the Speaker's payoffs with this new strategy:\pause 391 | \end{itemize} 392 | \begin{center} 393 | \begin{tabular}{r|cccc} 394 | &$Sub, S$ & $Sub, I$ & $Obj, S$ & $Obj, I$ \\\hline\hline 395 | Active & $c$ & $-i$ & $0$ & $c-i$ \\ 396 | Passive & $-p$ & $c-p-i$ & $c-p$ & $-p-i$ \\ 397 | Scramble & $0$ & $c-i$ & $c$ & $-i$ \\ 398 | \end{tabular} 399 | \end{center} 400 | \pause 401 | \begin{itemize} 402 | \item \textit{Scramble} \textbf{dominates} \textit{Passive} as a strategy when it is available. 403 | \end{itemize} 404 | \end{frame} 405 | 406 | \begin{frame} 407 | \frametitle{Scrambling Game} 408 | \scramblegame 409 | \end{frame} 410 | 411 | \begin{frame} 412 | \frametitle{Meta-game Thinking}\pause 413 | 414 | \begin{itemize} 415 | \item There are clear Schelling Points in this game: No matter what Nature chooses, the Speaker and Hearer can \emph{always} get to $c,c$ with no costs.\pause 416 | \item The Speaker will want to put the Hearer on track to get to this payoff.\pause 417 | \item And the Hearer knows no matter what, this will always be a payoff given by choosing \textit{Surface} (since \textit{Inverse} \emph{always} yields a $-i$).\pause 418 | \begin{itemize} 419 | \item Hearer: Always choose \textit{Surface}\pause 420 | \item Speaker: Always choose what strategy will yield $c,c$ when the Hearer chooses \textit{Surface}.\pause 421 | \end{itemize} 422 | 423 | \item No ambiguity ever---every sentence is unambigous and surface scope. 424 | \end{itemize} 425 | \end{frame} 426 | 427 | \section{Rigidity is Ambiguity} 428 | 429 | \begin{frame} 430 | \frametitle{Generalization}\pause 431 | \begin{itemize} 432 | \item From the Game Theoretics of this we can generalize:\pause 433 | \begin{exe} 434 | \ex Word order rigidity ${\rightarrow}$ ambiguity\pause 435 | \ex Word order flexibility ${\rightarrow}$ disambiguation\pause 436 | \end{exe} 437 | 438 | \item This is not just a ``parameter'', but a principle of order independent of formal syntactic properties of languages.\pause 439 | \item The Game Theoretics should be constant across \emph{not just} rigid/flexible languages, but across rigid/flexible constructions. 440 | \end{itemize} 441 | \end{frame} 442 | 443 | \begin{frame} 444 | \frametitle{English negation}\pause 445 | 446 | \begin{itemize} 447 | \item English negation may only appear \emph{after} a modal:\pause 448 | \begin{exe} 449 | \ex Billy can not go. \label{cannot}\hfill ($\neg >$ can; can $> \neg$) \pause 450 | \ex[*]{Billy not can go.\label{badneg}}\pause 451 | \end{exe} 452 | 453 | \item But where there are multiple modals, there are different places the negation can appear and there is only one interpretation available, just like the scrambling data:\pause 454 | 455 | \begin{exe} 456 | \ex Billy could not have gone before we arrived. \hfill ($not>have$)\pause 457 | \ex Billy could have not gone before we arrived.\hfill ($have>not$) 458 | \end{exe} 459 | \end{itemize} 460 | 461 | \end{frame} 462 | 463 | \begin{frame} 464 | \frametitle{Chinese local rigidity}\pause 465 | 466 | \begin{itemize} 467 | \item Normally, Chinese exhibits scrambling-style surface scope:\pause 468 | \begin{exe} 469 | \ex \begin{xlist}\label{chin} 470 | \ex[]{\gll Meigeren dou zhuazou yige {n\"uren}.\\ 471 | everyone all arrest a woman\\ 472 | \trans{``Everyone arrested a woman.''\label{chin1}} 473 | }\pause 474 | \ex[]{\gll (You) yige {n\"uren} meigeren dou zhuazou.\\ 475 | (have) a woman everyone all arrest.\\ 476 | \trans{``A woman was arrested by everyone.''\label{chin2}} 477 | }\end{xlist} 478 | \end{exe}\pause 479 | 480 | \item But in certain constructions, which are rigid, ambiguity arises:\pause 481 | 482 | \begin{exe} 483 | \ex{ \begin{xlist} 484 | \ex[]{\gll Meigeren dou bei yige {n\"uren} zhuazou.\\ 485 | everyone all PASS a woman arrest\\ 486 | \trans{``Everyone was arrested by a woman.''\label{chin3}} 487 | }\pause 488 | \ex[*]{Bei yige {n\"uren} meigeren dou zhuazou.\\ 489 | PASS a woman everyone all arrest\\ 490 | \label{chin4} 491 | }\end{xlist}} 492 | \end{exe} 493 | \end{itemize} 494 | \end{frame} 495 | 496 | \begin{frame} 497 | \frametitle{Persian local rigidity}\pause 498 | 499 | \begin{itemize} 500 | \item Persian is a scrambling language, but negation is stuck at the end with the ver, being rigid:\pause 501 | 502 | \begin{exe} 503 | \ex {\gll Yek d\=aneshju \=an ket\=ab-r\=a na-x\=and. \\ 504 | one student that book-ACC not-read \\ 505 | \trans{``A student didn't read that book.\label{par}''}} 506 | \end{exe}\pause 507 | \item \emph{But}, you do have an amount of flexibility with movement verbs. In those cases, flexibility remove ambiguity.\pause 508 | 509 | \begin{exe} 510 | \ex{\gll Billy na-raft hame shahr-i.\\ 511 | B. not-went all city-IND\\ 512 | \trans{``Billy didn't go to every city.'' \hfill ($\neg > \forall$; *$\forall > \neg$)\label{pm1}} 513 | }\pause 514 | \ex{\gll Billy be hame shahr-i na-raft.\\ 515 | B. to all city-IND not-went.\\ 516 | \trans{``Billy didn't go to any city.'' \hfill ($\forall > \neg$; *$\neg > \forall$)\label{pm2}} 517 | } 518 | \end{exe} 519 | \end{itemize} 520 | \end{frame} 521 | 522 | \begin{frame} 523 | \frametitle{Generalizations}\pause 524 | 525 | \begin{figure} 526 | \begin{tabular}{ll} 527 | Rigid Constructions & Flexible Constructions \\\hline\hline\pause 528 | English main clauses & Main clauses in scrambling languages \\\pause 529 | Persian negation & Chinese negation \\\pause 530 | Typical English negation & English negation around auxes \\\pause 531 | Chinese passives & English passives*\\\pause 532 | \textbf{All of these are ambiguous} & \textbf{All of these are non-ambiguous}\\ 533 | \end{tabular}\pause 534 | \end{figure} 535 | 536 | \begin{itemize} 537 | \item This is probably the most prominent empirical statement of my theory; I think it's borne out by typological data.\pause 538 | \item Passives as a ``bad'' strategy. 539 | \end{itemize} 540 | \end{frame} 541 | 542 | 543 | \section{Expansion} 544 | 545 | \begin{frame} 546 | \frametitle{Toward a General Theory of Quantifier Scope}\pause 547 | 548 | \begin{itemize} 549 | \item This account is incomplete. Notably it misses:\pause 550 | \begin{itemize} 551 | \item The tendency for universal and existential quantifiers to behave differently.\pause 552 | \item The tendency for some quantifiers of either type to prefer a certain range of scope (wide or narrow).\pause 553 | \end{itemize} 554 | \item On the first point, there have been some attempts \parencite{clark12} to implement this in Game Theory.\pause 555 | \item The second point can be dealt with in Evolutionary Game Theory, that is, languages have different quantifiers and conventionalize them as preferring one scope or another. This also can tell us \emph{why} different languages have ``synonymous'' quantifiers.\pause 556 | \item Combine my account here with the other two pieces and you would have a phenomenologically complete theory of quantification. 557 | \end{itemize} 558 | \end{frame} 559 | 560 | \begin{frame} 561 | \frametitle{References} 562 | \printbibliography 563 | \end{frame} 564 | 565 | \end{document} 566 | -------------------------------------------------------------------------------- /changes: -------------------------------------------------------------------------------- 1 | + Initial citation of Karimi 2003 is now specific with page number and direct quote of relevant statement. 2 | + Citation of Karimi 2003 on page 11 now uses sentences directly from source, with explanation afterwards of why the judgments differ. 3 | + Quotation of Aoun and Li 1989 on page 17 moved down to page 18 to relevant sentence. Page number added. 4 | + Ernst citation moved to example. 5 | -------------------------------------------------------------------------------- /distict.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/distict.pdf -------------------------------------------------------------------------------- /distict.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | 3 | \title{Distinctness Proposal} 4 | \author{Luke Smith} 5 | \date{Fall 2017} 6 | 7 | \begin{document} 8 | 9 | \maketitle 10 | 11 | \section{Abstract of Prelim 1} 12 | 13 | \begin{abstract} 14 | Here I argue that the concept of narrowly syntactic parameters is unnecessary, and unbefitting of a Minimalist model of the language faculty. 15 | I attempt to describe an area of language classically thought of as being syntax-qua-syntax, that is, word order, and argue that the word order differences found in different languages can be said to be derived from differing prosodic constraints. 16 | To implement this, I craft an Optimality Theoretic account of the canonical word order of sentential constituents (the subject, object and verb), which closely approximates the real-world typology of existing languages, all motivated by phonological principles already existing, or with close analogs in the literature. 17 | That is, pre-existing prosodic constraints are sufficient to determine a language's word order. 18 | I also show the enormous theoretical gains of this type of approach, noting the economy not just gained in theoretical simplicity, but in the clear account of how language is acquired by infants, that is, by a kind of robust phonological bootstrapping. 19 | \end{abstract} 20 | 21 | \section{Abstract of Prelim 2} 22 | 23 | \begin{abstract} 24 | Here I argue that the commonly (and uncommonly) known facts about the availability of quantifier scope interpretations fall out cleanly from communicative constraints which Speakers and Hearers tactically navigate to converge on the intended meaning of an utterance. 25 | This allows a relatively complete and motivated theory of quantifier scope ambiguity wholly without the need to resort to syntactic structure \textit{per se} for the main data. 26 | I model this theory Game Theoretically, in a game where speakers receive a payoff for successful communication, and decrements to payoffs for the use of marked constructions. 27 | These assumptions are sufficient to account for classical scope ambiguity data, but also newly compiled data I present which argues that \emph{word order rigidity}, across languages and constructions is the cause of scope ambiguity. 28 | \end{abstract} 29 | 30 | 31 | 32 | \section{Explanation of Distinctness} 33 | 34 | My first prelim is built principally on the data problem of differing word-orders across languages, the main analytical tool used being conventional Optimality Theory. The argument and intuition of the paper is that established prosodic constraints are sufficient for accounting for and motivating different word orders across languages, and also yiled a typology of word orders quite similar to that in the real world. 35 | 36 | My second covers data of quantifier scope ambiguity and how it differs between an in different languages. For this I've used an analytical tool relatively unused in linguistics generally: that is Game Theory. The main goal is replacing inconsistent derivationally-based accounts of scope differences with a more plausible and motivated pragmatic model, built on speakers receiving payoffs or payoff reductions from effective communication or marked constructions respectively. 37 | 38 | Besides the thematic commonality of desired theoretical economy, the data problems and tools in both papers are totally non-overlapping and dissimilar. 39 | 40 | To sum up: 41 | 42 | \begin{tabular}{r||cc} 43 | &Prelim 1&Prelim 2\\\hline\hline 44 | Data&Word order&Quantifier scope\\ 45 | Subfield&Syntax or prosody&Pragmatics or semantics\\ 46 | Tools&Optimality Theory&Game Theory\\ 47 | \end{tabular} 48 | 49 | \end{document} 50 | 51 | -------------------------------------------------------------------------------- /hend2012_SuB-pragmatics-quantifier-scope.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/hend2012_SuB-pragmatics-quantifier-scope.pdf -------------------------------------------------------------------------------- /luke_synsalon.md: -------------------------------------------------------------------------------- 1 | # Scope w/o Syntax: A Game Theoretic Approach 2 | 3 | ## Luke Smith---September 27, 2017 4 | 5 | Here I develop a novel and putatively universal framework for analysing and predicting the availability of quantifier scope ambiguity, formalized in **Game Theory**. 6 | 7 | Specifically, available scope interpretations are *not* licensed or restricted by the narrow syntax, rather are gradually weeded out by a strategic assessment of other interlocutors' communicative intent. That is, speakers word sentences in such a way to avoid marked constructions and communicate the intended interpretation of their sentence with the most clarity; hearers can intuit the intentions of the speaker by implicitly analysing how a speaker navigates these constraints. 8 | 9 | I employ Game Theory to analyse these strategic behaviors and derive several cross-linguistic empirical generalizations from this. Chief among which is the general fact that **syntactic rigidity causes ambiguity**, while equivalently, **syntactic flexibility disambiguates**. In formal terms, each available scope interpretaion is a Nash Equilibrium; if there is only one Nash Equilibrium, the sentence is unambiguous. 10 | 11 | I also propose some ways to further generalize the theory to a complete framework of scope analysis, integrating world knowledge and other pragmatic factors. 12 | -------------------------------------------------------------------------------- /luke_synsalon.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/luke_synsalon.pdf -------------------------------------------------------------------------------- /luke_synsalon_pres.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/luke_synsalon_pres.pdf -------------------------------------------------------------------------------- /mas: -------------------------------------------------------------------------------- 1 | Dear Luke, 2 | these are some reflections on your interesting and highly original work in progress on game theory and scope. The French cognitive anthropologist Dan Sperber has analyzed conversation and relevance in terms of game theory. 3 | 4 | Is it really a pragmatic issue, or rather an issue of the interfaces between syntax, SM and IC? 5 | 6 | Is “cost” additional computation? Or is it temporary failure to understand? 7 | 8 | The battle of the sexes has two Nash equilibria. How do you want to deal with these? It can have one only, if you introduce probabilities (mixed strategies). Can ambiguity be approached by means of probabilities (the default/preferred more probable interpretation versus the marked, less probable interpretation)? 9 | 10 | What about scalar implicatures? Can you treat them game-theoretically? 11 | 12 | German is not really a scrambling language (unlike Persian). The scrambling is limited to the Mittelfeld (middle field). Alessandra Tomaselli has interesting papers on this. 13 | 14 | An interesting case of an ambiguous word in English is “unlockable” (ask Dave Medeiros for details). It can mean impossible to lock or possible to unlock. A deviation from the overwhelming generality that negation is always the top morpheme, with widest scope. See work by Anna Maria di Sciullo. Inedible means impossible to eat, unpublishable means impossible to publish etc. We do not have something like *ediimble hypothetically meaning possible not to eat, and similar. This appears to be a linguistically universal morpho-lexical property. 15 | 16 | You mention, just mention, negative polarity items. Do you plan to develop this? 17 | 18 | On page 12, top, you say: “Such a framework would be able to maintain the statement that human language, at its syntactic core, should be independent of linear order, as the linear order effects are part of the pragmatic traits of language use and discourse.” 19 | Well, word order is not in the syntactic core, fine, but it’s not pragmatic, it’s an issue of the interface with SM. 20 | 21 | There is an interesting issue with “only”. Presuppositional or existential? It does not instantiate the conservativity/intersectivity universal (see work by Higginbotham and May, I sent you one piece). Chierchia has argued that it’s not a quantifier, so no problem that it’s not intersective, while Elena Herburger, in her essay “What Counts”, says it is, having its restriction on non-focused material, as shown by adjectivization and adverbials “only young angels have wings” you focus on old angels, “only rarely does he come”, you focus on events of his not-coming. Have a look at that. Maybe your approach can say something new. 22 | 23 | More on all this when we meet 24 | Massimo 25 | 26 | 27 | 28 | 29 | On 9/13/17, 9:36 AMMountain Standard Time, "Luke Smith" wrote: 30 | 31 | I don't think I'll be able to come today, but I'll come next week having 32 | consulted the artilces you sent me. 33 | 34 | Best, 35 | Luke 36 | 37 | On 09/12 11:17, Piattelli-Palmarini, Massi - (massimo) wrote: 38 | > Sure, it’s tomorrow Wednesday 10am to Noon, or next Wednesday 39 | > Massimo 40 | > 41 | > On 9/12/17, 4:17 PMMountain Standard Time, "Luke Smith" wrote: 42 | > 43 | > Thank you for understanding. 44 | > 45 | > I may also possibly come to your next office hour for discussion about 46 | > the prelim or the paper in this class. 47 | > 48 | > Luke 49 | > 50 | > On 09/12 11:10, Piattelli-Palmarini, Massi - (massimo) wrote: 51 | > > Dear Luke, 52 | > > sorry for the electronic mishap. Glad to receive these questions and the paper. Sure, I will be glad to be a member of the committee. I will manually insert a 100% grade into D2L for each. Very good questions that I will forward to the spaekers. I hope you will have no electronic problems in the future. As to your questions about my presentation, I will get back to you soon about them 53 | > > Massimo 54 | > > 55 | > > On 9/12/17, 4:02 PMMountain Standard Time, "Luke Smith" wrote: 56 | > > 57 | > > Hello Massimo, 58 | > > 59 | > > Tom informed me earlier that you had not received my question 60 | > > (apparently my email had been marking your emails from D2L as spam, so I 61 | > > did not see them, I have fixed this now). 62 | > > 63 | > > Attached are the three assignment sets. I apologize, but it seems that I 64 | > > was trying to submit them as markdown, which D2l did not accept. I would 65 | > > appreciate it if you accepted these at least at partial credit, but 66 | > > regardless, in the submission for the first lecture (by you) I 67 | > > superficially suggested a topic proposal for the research paper in the 68 | > > class which I would like to talk to you about at some point. 69 | > > 70 | > > Additionally, Tom may have mentioned this to you already, but I am 71 | > > contemplating doing a qualifying paper based on the paper I wrote for 72 | > > your class a year ago, specifically on a Game Theoretic analysis of 73 | > > quantifier scope ambiguity. I think that you would be a very beneficial 74 | > > committee member, and I was wondering if you'd like to discuss the 75 | > > project. (As a reminder, the original paper is attached.) 76 | > > 77 | > > Best, 78 | > > Luke 79 | > > 80 | > > 81 | > 82 | > 83 | 84 | 85 | -------------------------------------------------------------------------------- /peercomments/JRAY-COMMENT-luke_prelim2_Draft1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/peercomments/JRAY-COMMENT-luke_prelim2_Draft1.pdf -------------------------------------------------------------------------------- /peercomments/gmp_comments.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/peercomments/gmp_comments.pdf -------------------------------------------------------------------------------- /peercomments/jr_review.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/peercomments/jr_review.pdf -------------------------------------------------------------------------------- /peercomments/luke_prelim2_Draft1_McKayComments.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/peercomments/luke_prelim2_Draft1_McKayComments.pdf -------------------------------------------------------------------------------- /prelim2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/prelim2.pdf -------------------------------------------------------------------------------- /prelim2.tex: -------------------------------------------------------------------------------- 1 | % xelatex 2 | \documentclass{article} 3 | \usepackage[utf8]{inputenc} 4 | \usepackage{ot-tableau} 5 | \usepackage[backend=biber, style=authoryear-icomp]{biblatex} 6 | \usepackage{forest} 7 | \usepackage[normalem]{ulem} 8 | \usepackage{tikz} 9 | \usepackage{easylist} 10 | \usepackage{hanging} 11 | \usepackage{hyperref} 12 | \usepackage{blindtext} 13 | \usepackage{tipa} 14 | \usepackage{cgloss4e} 15 | \usepackage{gb4e} 16 | \usepackage{qtree} 17 | \usepackage{enumerate} 18 | \usepackage{longtable} 19 | \usepackage{dialogue} 20 | \usepackage{textgreek} 21 | \usepackage{framed} 22 | \usepackage{amsmath} 23 | \addbibresource{$HOME/Documents/LaTeX/uni.bib} 24 | 25 | \usetikzlibrary{calc} 26 | \usetikzlibrary{matrix} 27 | \usetikzlibrary{positioning} 28 | 29 | \definecolor{shadecolor}{gray}{.80} 30 | 31 | 32 | \usetikzlibrary{shapes.geometric, arrows, trees} 33 | 34 | \tikzset{Above/.style={midway,above,font=\scriptsize,text width=1.5cm,align=center,},Below/.style={midway,below,font=\scriptsize,text width=1.5cm,align=center}} 35 | \tikzstyle{box} = [rectangle, centered, draw=black,minimum width=3cm, minimum height=1cm] 36 | \tikzstyle{arrow} = [thick,->,>=stealth] 37 | 38 | 39 | \tikzset{centered/.style=} 40 | 41 | \title{Scope without Syntax: A Game Theoretic Approach} 42 | \author{Luke M. Smith} 43 | 44 | \begin{document} 45 | 46 | \maketitle 47 | 48 | \begin{abstract} 49 | Here I argue that the commonly (and uncommonly) known facts about the availability of quantifier scope interpretations fall out cleanly from communicative constraints which Speakers and Hearers tactically navigate to converge on the intended meaning of an utterance. 50 | This allows a relatively complete and motivated theory of quantifier scope ambiguity wholly without the need to resort to syntactic structure \textit{per se} for the main data. 51 | I model this theory game theoretically \parencite{neumann44}, in an extensive game \parencite{hart92} where speakers receive a payoff for successful communication, and decrements to payoffs for the use of marked constructions. 52 | These assumptions are sufficient to account for classical scope ambiguity data, but also newly compiled data I present which argues crucially that \emph{word order rigidity}, across languages and constructions is the cause of scope ambiguity. 53 | \end{abstract} 54 | 55 | %\section{Problems with syntactically-derived accounts of scope} 56 | 57 | %\begin{exe} 58 | %\ex 59 | %\begin{xlist} 60 | %\ex Many of the arrows didn't hit the target. 61 | %\ex The target wasn't hit by many of the arrows. 62 | %\end{xlist} 63 | %\end{exe} 64 | 65 | %\begin{exe} 66 | %\ex 67 | %\begin{dialogue} 68 | %\speak{Speaker 1} Look at the target: it wasn't hit by your arrow! 69 | %\speak{Speaker 2} The target wasn't hit by many of the arrows. 70 | %\end{dialogue} 71 | %\end{exe} 72 | 73 | \tableofcontents 74 | 75 | \listoffigures 76 | 77 | %\section{Need for a novel approach to scope} 78 | 79 | 80 | %Here I will argue that an account of quantifier scope ambiguity as a produce or part of the syntactic engine is not necessarily, and these scope effects can be modeled as naturally falling out from several pragmatic assumptions. 81 | 82 | 83 | %The provenience of this account is based in some existential and empirical shortcomings with traditional accounts to scope phenomena. 84 | %Firstly, quantifier scope, while it sometimes seems to correlate with deeper syntactic traits, has some traits that make it markedly incompatible with rigorously Minimalist approach to syntax. 85 | %Chief among which is the f 86 | 87 | 88 | 89 | 90 | 91 | 92 | %I've decided to add this section at the last minute. It will briefly overview some of the problems behind traditional generative attempts at modeling scope, chiefly: 93 | 94 | %\begin{itemize} 95 | %\item The marked unsystaticity of scope as an indicator of syntactic phenomena, i.e. that there still isn't a commonly accepted metric for what scope effects syntactic movements, etc. should have. 96 | %\item The sensitivity of scope to linear order. 97 | %\item The ubiquitous ``Chomsky's Aphasia'' in scope judgments and non-categorical judgments. 98 | %\end{itemize} 99 | 100 | \section{The Uniqueness of Quantifier Scope} 101 | 102 | Quantifier scope ambiguity is often treated as a syntactic phenomenon, or at least a syntactic \emph{epi}phenomenon, but it bears some fairly marked traits that make a complete theory of quantifier scope incompatible with a rigorous formal approach to syntax. 103 | 104 | Firstly, quantifier scope is known to be highly sensitive to linear order. 105 | This is a generalization true generally, but especially true of languages with free word order 106 | \parencite{pafel04}. 107 | \textcite[xix]{karimi03} in fact notes that one of the ``specific properties'' of scrambling languages is that ``scope is usually determined by surface (derived) positions of quantifiers.'' 108 | However in a narrowly Minimal interpretation of language, the phonological representation of a sentence, including the linear order of words, \emph{should} be incidental, but in any case not a factor that contributes to or limits a sentence's meaning. 109 | 110 | At that, while it's very common for syntacticians to evoke scope judgments in arguments about syntactic features, there is no systematic metric for what syntactic operations trigger scope judgments or \textit{vice versa}. 111 | Refer to the literature ensuing after \textcite{han07}'s interesting study in which it was argued that Korean speakers internalize two different grammars (due to poverty of stimulus) and as such exhibit different quantifier scope judgments. 112 | One population of speakers allowed for an additional type of ambiguity that the other population consistently rebuffed. 113 | That said, the debate arose as to \emph{which} population was the one with the extra reading: did low verbs create ambiguity, or did verbs in T? 114 | While an empirical difference had been noticed, and formal tools existed to account for some distinction, the lack of systematic use of quantifier scope in syntactic theory makes references to scope only incidental. 115 | 116 | At that scope is simply empirically problematic if we assume it is an output of the syntax. 117 | While some sentences are acceptable and some clearly unacceptable, scopal readings are notoriously unclear, context-dependent and generally victims of whim. 118 | 119 | For these reasons, it's sensible to look at scope as a phenomenon conditioned not so much by syntax, but by pragmatics and context. 120 | This is my goal. 121 | Using Game Theory \parencite{neumann44,hart92} I will attempt to craft a model of what communicative factors are sufficient to account for different possible quantifier scope readings. 122 | 123 | \section{Assumptions\label{assump}} 124 | 125 | 126 | Before proceeding, I'll make some \emph{a priori} assumptions about scope interpretations. 127 | We will see that much of the diversity of scope can be accounted for merely taking these as assumptions interacting with each other. 128 | 129 | \begin{enumerate} 130 | \item Speakers and listeners prefer for quantifiers to be in ``surface scope'' order. 131 | \item ``Transformations'' classically named (e.g. passives) are ``costly'' or ``dispreferred'' in some sense. 132 | \item ``Scrambling'' in languages which exhibit it, is not similarly costly. 133 | \end{enumerate} 134 | 135 | Before explaining the model, it's at least worth justifying all three of these on functional grounds. 136 | These are simply \textit{just so} justifications of these assumptions, none of which are fundamental to our argument here. 137 | It is not important \emph{why} these assumptions are true, only that they are decent priors for our model here. 138 | 139 | \subsection{Preference for Surface Scope} 140 | 141 | As noted above, languages have a general preference for surface scope interpretation, meaning that \textit{ceteris paribus}, if there are two quantifiers in a sentence, the first will tend to scope over the other. 142 | This can be justified in various ways, but perhaps most sensible is the idea that sentences are processed more or less linearly, and as words are interpreted, the language faculty or cognition generally proceeds to generate a mental schema or image for the sentence (similar to the ideas in \textcite{langacker87}). 143 | 144 | A sentence with surface scope will make this process easier, as otherwise one would have to revise one's mental image when the truly wide scope is accessed later in the sentence. 145 | 146 | \subsection{Transformations are ``marked''} 147 | 148 | With respect to transformations, a longstanding assumption of transformational grammar was that those utterances which are ``transformed'' are in some ways, more marked or at least are derived from simplex expressions. 149 | 150 | \begin{exe} 151 | \ex\label{caes} 152 | \begin{xlist} 153 | \ex Caesar crossed the Rubicon.\label{simp} 154 | \ex It was Caesar who crossed the Rubicon.\label{celft} 155 | \ex The Rubicon was crossed by Caesar.\label{pass} 156 | \end{xlist} 157 | \end{exe} 158 | 159 | That is, while all sentences in (\ref{caes}) share a semantically equivalent kernel, (\ref{simp}) is in someway more basic than the cleft (\ref{celft}) or the passive (\ref{pass}). 160 | Earlier ideas in Generative Grammar assumed that this was because (\ref{celft}) and (\ref{pass}) were literally derived from (\ref{simp}), thus leading to the psycholinguistic thesis of the Derivational Theory of Complexity, hypothesizing that the latter two sentences were marked as they are later formations of the first. 161 | 162 | While theories such as this have fallen out of favor in mainstream Generative Grammar, data from acquisition does indeed show that sentences such as (\ref{celft}) and (\ref{pass}) are acquired and employed at a distinctly later stage of language development. 163 | 164 | Still, for our purposes, we could say something as simple as (\ref{celft}) and (\ref{pass}) simply contain more morphemes or words than (\ref{simp}). 165 | We should be clear that the particular nature of the cost of ``transformations'' isn't important for us, only the general assumption that they are marked or dispreferrable. 166 | 167 | 168 | \subsection{Scrambling is not costly\label{scrambcost}} 169 | 170 | This may fall out for free depending on one's account of the costliness of transformations. 171 | For example, if we say that the passive is generally disprefered because it consists in adding additional morphemes and words to a clause, we implicitly say that scrambled sentences, since they require no additional morphology or periphrasis, are not similarly costly. 172 | One could make similar arguements based on frequency of construction or other discourse factors. 173 | 174 | \section{Basic English Data and Passives\label{eng}} 175 | 176 | With the background established, we can move to address data and spelling out this model. 177 | First note some rudimentary scope facts in English represented below: 178 | 179 | \begin{exe} 180 | \ex\label{first}{\begin{xlist} 181 | \ex Every man saw a girl. \hfill ($\forall > \exists$; $\exists > \forall$)\label{evman} 182 | \ex Everyone speaks two languages. \hfill ($\forall > 2$; $2 > \forall$)\label{evsp} 183 | \end{xlist}} 184 | \ex{\begin{xlist} 185 | \ex A girl was seen by every man. \hfill ($\exists > \forall$; *$\forall > \exists$)\label{agirl} 186 | \ex Two languages are spoken by everyone. \hfill ($2 > \forall$; *$\forall > 2$)\label{2lang} 187 | \end{xlist}} 188 | \end{exe} 189 | 190 | Generally, unmarked active ``kernel'' sentences like (\ref{evman}) and (\ref{evsp}) demonstrate fairly robust scope ambiguity. 191 | Thus, (\ref{evman}) can mean either that there is one particular girl that every man saw ($\exists>\forall$) or that each man saw a (potentially different) girl ($\forall>\exists$). 192 | 193 | In the ``transformed'' passive equivalents of the two sentences, however, syntactic ambiguity becomes unavailable and surface scope is typically the only sensible reading, as below. 194 | 195 | \begin{exe} 196 | \ex{\begin{xlist} 197 | \ex A man ate every watermelon. \hfill ($\exists>\forall$; $\forall>\exists$) 198 | \ex Every watermelon was eaten by a man.\label{passman} \hfill ($\forall>\exists$; ??$\exists>\forall$) 199 | \end{xlist}} 200 | \ex{\begin{xlist}\label{love} 201 | \ex Everyone loves someone. \hfill ($\forall>\exists$; $\exists>\forall$)\label{sent} 202 | \ex Someone is loved by everyone.\label{passsome} \hfill ($\exists>\forall$; ??$\forall>\exists$) 203 | \end{xlist}} 204 | \end{exe} 205 | 206 | Thus (\ref{agirl}) is only true if there was only one girl in question, while (\ref{2lang}) is only true if all of the people speak the same two particular languages. 207 | We see that this scopal alternation generally holds across most active/passive sentence pairs.\footnote{Some exceptions will be discussed later.} 208 | 209 | It should be said that while (\ref{passman}) and (\ref{passsome}) are labeled as requiring surface scope, there are indeed situations where the inverse readings are possible or required. 210 | While when some traditional accounts of scope categorically rule these sentences out, for me, what is important is that the inverse passive readings are simply \emph{highly dispreferred}. 211 | As our analysis will show, there is nothing formally syntactic that makes these sentences essentially bad, but merely the results of the game theoretic analysis. 212 | The important fact here is merely that English passives, without other context strongly imply only surface scope. 213 | 214 | 215 | \section{Model} 216 | 217 | It's important to be clear about the game theoretics of communication. 218 | Resolving scope ambiguities like that in (\ref{first}) is a kind of coordination game with imperfect information. 219 | That is, two interlocutors must converge on the same interpretation of a sentence which has been decided by circumstance; 220 | the Speaker knows the required interpretation and in speaking attempts to signal it to the Hearer. 221 | Both players ``win'' if the Speaker is succesful in leading the Hearer to the correct interpretation. 222 | If the speaker intends for a universal quantifier, such as \emph{every}, to scope over an existential one, such as \emph{some}, he ideally must word his sentence in such a way to communicate this. 223 | 224 | 225 | 226 | 227 | \begin{figure} 228 | \begin{center} 229 | \begin{tikzpicture}[node distance=2cm] 230 | 231 | \node (nature) [box, align=center] {{\large \textbf{ Player 0: ``Nature''}}\\Determines desired quantifier scope interpretation $s$}; 232 | \node (speaker) [box, align=center, below of=nature] {{\large \textbf{Player 1: ``Speaker''}}\\Determines a best wording $w$ to communicate $s$ }; 233 | \node (hearer) [box, align=center, below of=speaker] {{\large \textbf{Player 2: ``Hearer''}}\\Must guess $s$ based $w$}; 234 | 235 | \draw [arrow] (nature) -- (speaker) ; 236 | \draw [arrow] (speaker) -- (hearer) ; 237 | \end{tikzpicture} 238 | \end{center} 239 | \caption{The sequence of player choices\label{seq}} 240 | \end{figure} 241 | 242 | To be more specific, we can say this is a kind of 3-player coordination game (where the sequence is indicated in Figure \ref{seq}). 243 | The non-human Player 0, who we can term \textbf{Nature} dictates what the needed scope interpretation should be, that is, whether, based on circumstances, a subject quantifier must scope over an object quantifier, or \emph{vice versa} or any other combination of quantificational elements.\footnote{We will only be including subject and object quantification for sake of simplicity to outline some general principles.} 244 | Nature represents the needed discourse environment which neither the Speaker or Hearer determines themselves. 245 | We can think of the choice of Player 0, Nature, as a random or given element of the model. 246 | Player 1, \textbf{the Speaker}, knows what the needed scope given by Nature is, and has to encode a linguistic message to communicate it to Player 2: \textbf{the Hearer} who is ignorant of it (illustrated in Figure \ref{exten}). 247 | In each language, the Speaker might have different strategies usable to communicate this message, depending on the structure of a language.\footnote{Thus, our intent here is not to argue how or why a given sentence in a language is grammatical or acceptable, but why Speakers choose to use a given sentence to communicate a particular scope reading.} 248 | 249 | If the Hearer's interpreted scope and the scope selected by Nature match, both human players get a payoff (represented as $c$ for \emph{\textbf{c}ommunication}), while if they do not match, there has been a miscommunication and this there is no payoff. 250 | Similarly, we can formalize our assumptions in the Section \ref{assump}. 251 | If transformations, specifically passives, are costly or dispreferred in some way, we can model them as saying that they reduce the payoff to the speaker to some degree (designated by $-p$). 252 | Similarly, instances of free word order and so-called ``scrambling'' do \emph{not} reduce any payoff; this will be addressed in Section \ref{scramb}. 253 | Lastly, surface scope should be universally preferred, so in situations where a speaker and hearer settle on an \emph{inverse} scope reading of a sentence, their payoffs are reduced by some degree (symbolized by $-i$). 254 | 255 | We should also assume that $c > (p + i)$, meaning that it is always preferable for the two interlocutors to understand each other even if transformations and inverse scope may dig into that payoff. 256 | Also, $p$ and $i$ are not necessarily larger or smaller than one another, and may vary from situation to situation, meaning that in some situations, it may be preferable for a speaker to vie for inverse scope rather than performing a transformation, while in others, it opposite may be true. 257 | 258 | The particulars of an instantiation of the game are based in the structure of whatever language is being spoken. 259 | For any given language, there will be a different set of syntactically valid utterances that the Speaker can use to signal to the Hearer what the intended scope is. 260 | Given the constraints posited above, we will assume that surface scope is the ideal, but different languages differ in their abilities to use different transformations or scrambling. 261 | 262 | 263 | \subsection{The Game Theoretic Core} 264 | 265 | Now, given our constraints and model above, we can derive these facts of the difference between actives and passives from the interaction of strategic interpretation on the part of the two interlocutors. 266 | Assume the three player game above (of Nature, a Speaker and a Hearer), dealing with the kernel sentence in (\ref{sent}) ``Everyone loves someone,'' depicted in the decision tree in Figure \ref{exten}. 267 | 268 | First, the Nature player determines whether the intended scope of the utterance should be where the universal quantifier takes wide scope ($\forall>\exists$, or $Sub > Obj$) or where the existential does ($\exists>\forall$, or $Obj > Sub$). 269 | Then the Speaker, aware of Nature's choice, takes his turn choosing either to word the sentence as the active ``Everyone loves someone'' or the passive ``Someone is loved by everyone''. 270 | Lastly, the Hearer, unaware of Nature's original decision, chooses whether to interpret the sentences with surface scope or inverse scope. 271 | 272 | To repeat, if the Hearer guesses the correct scope as defined by Nature, both the Speaker and Hearer receive a payoff of $c$. 273 | If the players fail to engineer this, both will receive no payoff. 274 | Additionally, because a passive transformation is ``costly,'' the payoff of the Speaker will be deducted by $p$ whenever he chooses to produce a passive. 275 | Lastly, if the dispreferred inverse scope has to be employed, both speakers will have a penalty of $i$. 276 | 277 | \begin{figure} 278 | \begin{tabular}{r||l} 279 | Abrv.& Strategy name\\\hline\hline 280 | A & \textbf{A}ctive Voice (Speaker)\\ 281 | P & \textbf{P}assive Voice (Speaker)\\ 282 | S & Interpret \textbf{S}urface scope (Hearer)\\ 283 | I & Interpret \textbf{I}nverse scope (Hearer)\\ 284 | $Sub > Obj$ & Demand the subject scope over the object (Nature)\\ 285 | $Obj > Sub$ & Demand the object scope over the subject (Nature)\\ 286 | \end{tabular} 287 | \caption{The strategies for each player and their abbreviations} 288 | \end{figure} 289 | 290 | 291 | \begin{figure} 292 | \begin{center} 293 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 294 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 295 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 296 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 297 | \begin{tikzpicture} 298 | \node {Nature} 299 | child{ 300 | node{Speaker} 301 | child{ 302 | node(d){Hearer} 303 | child{ 304 | node{$\displaystyle\binom{c}{c}$} 305 | edge from parent 306 | node[left]{$S$} 307 | } 308 | child{ 309 | node{$\displaystyle\binom{-i}{-i}$} 310 | edge from parent 311 | node[right]{$I$} 312 | } 313 | edge from parent 314 | node[left]{$A$} 315 | } 316 | child{ 317 | node(a){Hearer} 318 | child{ 319 | node{$\displaystyle\binom{-p}{0}$} 320 | edge from parent 321 | node[left]{$S$} 322 | } 323 | child{ 324 | node{$\displaystyle\binom{c-p-i}{c-i}$} 325 | edge from parent 326 | node[right]{$I$} 327 | } 328 | edge from parent 329 | node[right]{$P$} 330 | } 331 | edge from parent 332 | node[left]{${Sub}>{Obj}$} 333 | } 334 | child{ 335 | node{Speaker} 336 | child{ 337 | node(b){Hearer} 338 | child{ 339 | node{$\displaystyle\binom{0}{0}$} 340 | edge from parent 341 | node[left]{$S$} 342 | } 343 | child{ 344 | node{$\displaystyle\binom{c-i}{c-i}$} 345 | edge from parent 346 | node[right]{$I$} 347 | } 348 | edge from parent 349 | node[left]{$A$} 350 | } 351 | child{ 352 | node(c){Hearer} 353 | child{ 354 | node{$\displaystyle\binom{c-p}{c}$} 355 | edge from parent 356 | node[left]{$S$} 357 | } 358 | child{ 359 | node{$\displaystyle\binom{-p-i}{-i}$} 360 | edge from parent 361 | node[right]{$I$} 362 | } 363 | edge from parent 364 | node[right]{$P$} 365 | } 366 | edge from parent 367 | node[right]{${Obj}>{Sub}$} 368 | }; 369 | \draw [dashed](d)to[in=180](b); 370 | \draw [dashed](a)to[in=180](c); 371 | \end{tikzpicture} 372 | \end{center} 373 | \caption{The extensive game\label{exten} in English} 374 | \end{figure} 375 | 376 | \begin{figure} 377 | \begin{shaded} 378 | \small 379 | \subsection*{Notes on the Game Tree} 380 | Each branch represents a player choice. Payoffs to the Speaker and the Hearer are at each terminal node, the Speaker's being on top and the Hearer's below.\\ 381 | 382 | The dotted lines represent the equivalence classes for the Hearer. That is, they unite the nodes that the Hearer can not distinguish. To be clear, if the Speaker chooses the ``Active'' strategy, the Hearer knows he must be on the nexus either first or third from left, but can't distinguish between the two since he is unaware of Nature's original choice. 383 | \caption{A primer on extensive game theory notation as in Figure \ref{exten}\label{expl}} 384 | \end{shaded} 385 | \end{figure} 386 | 387 | 388 | Since this decision tree involves three players with substantive choices, it helps to narrow down the decision to find Nash Equilibria, Schelling Points or notable strategies. 389 | Let's put ourselves in the position of the Hearer. 390 | The Hearer is the one dealing with the informational asymmetry guessing the choice of Nature given the Speaker's utterance. 391 | Given the aforementioned decision tree in Figure \ref{exten}, the Hearer can make two hypotheses about Nature, that it chose to demand that the subject/agent scope over the object/patient, or that it demands that the object should scope over the subject. 392 | 393 | The key to the strategy is the cost of the passive $p$. 394 | Let's take the situation when Nature selects $Sub>Obj$. 395 | In that case, the hypothetical active form ``Everybody loves someone'' already has the correct surface scope order. 396 | While it is not immediately sure that the Hearer would determine that this active clause is indeed the required order, it costs the Speaker neither decrements of $p$ or $i$. 397 | 398 | If the Speaker were to passivize the sentence to ``Someone is loved by everybody'', not only would he be incurring the loss of $p$ for the passive transformation, but if the Hearer did guess correctly that the sentences should have \emph{inverse} scope in this reading, both players would additionally be losing $i$. 399 | 400 | \begin{figure} 401 | \begin{shaded} 402 | \small 403 | \subsection*{Game Theoretic Terms} 404 | 405 | \textbf{Imperfect information} -- When at least one player is not perfectly aware of the actions of another. In our game, the Hearer is not aware of the decision of Nature, ergo this is a game with imperfect information. 406 | 407 | \textbf{Incomplete information} -- When at least one player is not aware of the payoffs for a player. Although this concept is frequently confused with imperfect information, we \emph{do not} have a incomplete information game. 408 | 409 | \textbf{Signalling} -- When a player voluntarily undergoes a costs to communicate his tactics or strength. For example, a zebra, noticing a stalking lion may ``irrationally'' jump up and down in place instead of running to show his spriness and tell the lion he isn't an easy target. 410 | 411 | \textbf{Nash Equilibrium} -- A point in a game where no player can improve his position by changing strategies given what he knows. While Nash Equilibria are usually the MacGuffin of game theoretic analysis, our game has no proper Nash Equilibrium (not assuming iteration). The concept is usually attributed to \textcite{nash50} (hence the name), but was originally formulated at least in \textcite{cournot38}'s theory of economic duopoly. 412 | 413 | \textbf{Schelling Point} -- Sometimes called a \textit{Focal Point}. A point which is not a Nash Equilibrium, but due to some meta-game reasoning is a particularly marked. Originally formulated in \textcite{schelling60}. 414 | 415 | \textbf{Equivalence Classes} -- In an Imperfect Information game (like this one) nodes in a decision tree that a player cannot distinguish due to his imperfect information. 416 | \end{shaded} 417 | \end{figure} 418 | 419 | The Speaker therefore is in a position of two theoretically uncertain outcomes, one that can yield him $c$, while the other can yield him only $c-p-i$. 420 | All things considered, $c$ is preferable, and therefore using the active sentence to express $Sub>Obj$ should be preferable. 421 | While this is not a proper Nash Equilibrium, since we are dealing with a non-simultaenous game, this decision can act as a \emph{signal} to the second player, the Hearer. 422 | 423 | The Hearer, knowing that there is this Schelling Point for choosing the active sentence when given ${Sub}>{Obj}$ can therefore conclude by deduction that if the Speaker for some reason chooses to word his sentence in the passive, it is nearly certain that Nature meant \emph{the other} alternative: ${Obj}>{Sub}$. 424 | Or put more generally in (\ref{cost}). 425 | 426 | \begin{exe} 427 | \ex{\textit{A speaker will not engage in a costly transformation which yields an undesired scope order.\label{cost}}} 428 | \end{exe} 429 | 430 | 431 | 432 | %Figure \ref{some} gives a Hearer no conclusion about the Speaker's dominant strategy, it is simply a kind of \emph{Matching Pennies} game with the additional cost of the passive transformation.\footnote{There is the clear \emph{focal point} of the Speaker using an \emph{Active} and the Hearer interpreting inverse scope, but this is illusory given the random element of Nature and the wider tree in Figure \ref{tree}.} However, since we cannot \emph{rule out} the use of the passive, and we have already established (\ref{cost}), we can also logically conclude (\ref{pass}). 433 | Or to spell (\ref{cost}) out more specifically in our context, see (\ref{passa}). 434 | 435 | 436 | \begin{exe} 437 | \ex{\textit{The use of a costly reordering transformation, \emph{ceteris paribus}, entails that the underlying object should take wide scope over the subject. Or put another way, scopal ambiguity dissappears in favor of surface scope after a costly transformation.\label{passa}}} 438 | \end{exe} 439 | 440 | To put it in more intuitive terms, if the subject does something costly like passivization to a sentence, \emph{he is doing it for a reason}, specifically here to avoid the other loss of $i$. 441 | Passivizing only to also lose $i$ is not a good Schelling Point strategy. 442 | For this reason, in most pragmatic circumstances, passivized sentences appear as unambiguous, seeing that we conclude that they are motivated to avoid the cost of the inverse scope. 443 | 444 | In the situation where Nature chooses ${Obj}>{Sub}$, the situation is less clear. 445 | This is because the Speaker has two possible winning payoffs: $c-i$ and $c-p$, neither of which is necessarily preferable since we have not established whether $p>i$, nor do I think one is always larger than the other. 446 | In this situation, a Speaker could passivize and to avoid inverse scope order, or bite the bullet and take inverse scope without the passivization, both with uncertainty. 447 | The end result is that the active sentence ``Everyone loves someone'' does not clearly communicate whether Nature choose ${Sub}>{Obj}$ or ${Obj}>{Sub}$ since there is no obvious Schelling Point to rule out one of the strategies. 448 | Therefore, while the English passive is unambiguous due to the presence of a Schelling Point, the English active is not. 449 | 450 | \subsection{Scrambling\label{scramb}} 451 | 452 | But how should scope ambiguities work where there are ``costless'' ways of reordering quantified nominals? 453 | Scrambling languages present ways of reordering nominals without a marked transformation, as we have assumed in Section \ref{scrambcost}. 454 | In our model, Speakers in languages like this, such as German, Persian, Korean and Japanese, have access to another strategy aside from producing an active or passive clause. They may also \emph{scramble} the object such that it appears to the left of the subject. 455 | 456 | First a theoretical note. 457 | The ``scrambling'' tendencies of each of these languages may be different: German ``scrambling'' is quite different syntactically than Korean's, etc. 458 | This is not so important to us here. 459 | We only need to know if there is a valid reordering strategy in a language which is not marked in the way that passives are. 460 | Why German or Persian or other languages vary with respect to syntactic flexibility is not germane for us here, only the \emph{effects} of these traits on scopal possibilities. 461 | Our account here is not a theory of syntax, only of quantifier scope. 462 | 463 | \subsubsection{Scope in Scrambling Languages} 464 | 465 | First the empirical generalizations. 466 | German, a scrambling language shows a very different paradigm of scope availabilities than does English. 467 | Even in ``kernel'' sentences like (\ref{g}), surface scope is the only plausible interpretation. 468 | The same is true in the scrambled sentence (\ref{gs}), where the object has been scrambled left of the subject. 469 | 470 | \begin{exe} 471 | \ex{\gll dass eine Frau jeden liebt\\ 472 | that a woman everybody loves\\ 473 | \trans{``\ldots that some woman loves everyone\label{g}''\hfill (some $>$ every; ??every $>$ some)}} 474 | \ex{\gll dass jeden eine Frau liebt\\ 475 | that everybody a woman loves\\ 476 | \trans{``\ldots that a woman loves everyone\label{gs}'' \hfill (every $>$ some; ??some $>$ every)}} 477 | \end{exe} 478 | 479 | This universal surface scope is well mirrored in other languages. 480 | To repeat, as \textcite{pafel04,karimi03} among others note, the general tendency is for scrambling languages 481 | We can see similar patterns in Persian in (\ref{pers}). 482 | 483 | \begin{exe} 484 | \ex \begin{xlist} 485 | \label{pers} 486 | \ex {\gll Har d\=aneshjui b\=ayad ye mas'ala-ro hal bo-kon-e. \\ 487 | each student must a problem-r\=a solution SUBJ-do-3sg \\ 488 | \trans{``Each student must solve a problem.'' \hfill $({\forall}>{\exists}, ??{\exists}>{\forall})$}} 489 | \ex {\gll Ye mas'ala-ro har d\=aneshjui bayad hal bo-kon-e. \\ 490 | a problem-r\=a every student must solution SUB-do-3sg \\ 491 | \trans{``There's a problem that every student must solve.'' \hfill $({\exists}>{\forall}, ?{\forall}>{\exists})$}} 492 | \end{xlist} 493 | \end{exe} 494 | 495 | It should be noted that \textcite{karimi03} treats the latter sentence as ambiguous, a judgment I could not replicate with my consultants in context. 496 | Still the different judgment cited in \textcite{karimi03} is understandable given that the surface scope order $({\exists} > {\forall})$ logically entails the other $({\forall} > {\exists})$, and the use of \emph{har} ``every'', a quantifier with strong pragmatic preference for ``wide scope''. 497 | We will discuss this as a more general tendency in section \ref{prefscope}. 498 | 499 | 500 | %\begin{exe} 501 | %\ex\label{pers} \begin{xlist} 502 | %\ex {\gll Yek d\=aneshjui hame ket\=ab-i-ro x\=and. \\ 503 | %a student all book-IND read \\ 504 | %\trans{``A student read every book.''\hfill ($\exists > \forall$; *$\forall > \exists$)}} 505 | %\ex {\gll Hame ket\=ab-i-ro yek d\=aneshjui x\=and. \\ 506 | %all book-IND-ACC a student read \\ 507 | %\trans{``A student read every book.''\hfill ($\forall > \exists$; *$\exists > \forall$)}} 508 | %\end{xlist}\end{exe} 509 | 510 | Regardless, this generalization about scope effects is fairly well-accepted with respect to scrambling languages, but it can also be shown to fall out from our already mentioned assumptions. 511 | 512 | \subsubsection{An Account of Scramblible Scope\label{scbad}} 513 | 514 | In our game theoretic framework, we can say that the \emph{Scramble} strategy, which consists of moving the object left of the subject, achieves the linear order of passivization without the cost of $p$ to the Speaker (Section \ref{scrambcost}). 515 | Because of this, \emph{Scramble} in a scrambling language is always preferable to the dominated strategy \emph{Passive} for the Speaker; the payoffs are shown in Figure \ref{dom}. 516 | Therefore, a rational Speaker need not consider \textit{Passive} as an option for achieving the correct scope interpretation if the alternative strategy \textit{Scramble} is available. 517 | We will discuss some typological implications of this in Section \ref{passscr}. 518 | 519 | \begin{figure} 520 | \begin{shaded} 521 | \begin{center} 522 | \begin{tabular}{r|cccc} 523 | &$Sub, S$ & $Sub, I$ & $Obj, S$ & $Obj, I$ \\\hline\hline 524 | Active & $c$ & $-i$ & $0$ & $c-i$ \\ 525 | \sout{Passive} & $-p$ & $c-p-i$ & $c-p$ & $-p-i$ \\ 526 | Scramble & $0$ & $c-i$ & $c$ & $-i$ \\ 527 | \end{tabular} 528 | \end{center} 529 | \small For every pair of decisions made by other speakers, each payoff for the Speaker is greater if he chooses $Scramble$ than if he chooses $Passive$, due to the $-p$ penalty. 530 | \caption{$Scramble$ dominates $Passive$ as a strategy for Speaker\label{dom}} 531 | \end{shaded} 532 | \end{figure} 533 | 534 | \begin{figure} 535 | \begin{center} 536 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 537 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 538 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 539 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 540 | \begin{tikzpicture} 541 | \node {Nature} 542 | child{ 543 | node{Speaker} 544 | child{ 545 | node(d){Hearer} 546 | child{ 547 | node{$\displaystyle\binom{c}{c}$} 548 | edge from parent 549 | node[left]{$S$} 550 | } 551 | child{ 552 | node{$\displaystyle\binom{-i}{-i}$} 553 | edge from parent 554 | node[right]{$I$} 555 | } 556 | edge from parent 557 | node[left]{$A$} 558 | } 559 | child{ 560 | node(a){Hearer} 561 | child{ 562 | node{$\displaystyle\binom{0}{0}$} 563 | edge from parent 564 | node[left]{$S$} 565 | } 566 | child{ 567 | node{$\displaystyle\binom{c-i}{c-i}$} 568 | edge from parent 569 | node[right]{$I$} 570 | } 571 | edge from parent 572 | node[right]{$Sc$} 573 | } 574 | edge from parent 575 | node[left]{${Sub}>{Obj}$} 576 | } 577 | child{ 578 | node{Speaker} 579 | child{ 580 | node(b){Hearer} 581 | child{ 582 | node{$\displaystyle\binom{0}{0}$} 583 | edge from parent 584 | node[left]{$S$} 585 | } 586 | child{ 587 | node{$\displaystyle\binom{c-i}{c-i}$} 588 | edge from parent 589 | node[right]{$I$} 590 | } 591 | edge from parent 592 | node[left]{$A$} 593 | } 594 | child{ 595 | node(c){Hearer} 596 | child{ 597 | node{$\displaystyle\binom{c}{c}$} 598 | edge from parent 599 | node[left]{$S$} 600 | } 601 | child{ 602 | node{$\displaystyle\binom{-i}{-i}$} 603 | edge from parent 604 | node[right]{$I$} 605 | } 606 | edge from parent 607 | node[right]{$Sc$} 608 | } 609 | edge from parent 610 | node[right]{${Obj}>{Sub}$} 611 | }; 612 | \draw [dashed](d)to[in=180](b); 613 | \draw [dashed](a)to[in=180](c); 614 | \end{tikzpicture} 615 | \end{center} 616 | \caption{The extensive game\label{trees} in a scrambling language} 617 | \end{figure} 618 | 619 | Thus if we disregard the possibility of passivization as disprefered as a scope technique, once again, both human players have two possible choices. 620 | We should see that there is no straight-forward dominant strategy for either player, but a very obvious signalling opportunity arises in the meta-game, or a Schelling Point. 621 | 622 | Specifically, independent of the Speaker and Nature's choices, the Hearer will want to avoid choosing the \emph{Inverse} strategy. 623 | Given there is no Nash Equilibrium in the simple game, there is no clear dominant strategy for the Speaker, but even if a Hearer interprets his behavior as totally random, choosing the \emph{Surface} strategy increases the average payoff for the Hearer. 624 | The Speaker realizes this (and shares the desire to avoid $-i$) and can strategically select his strategy based on what will require the Hearer to \emph{not} select the \emph{Inverse} strategy. 625 | This acts as a signal to the Hearer, or more generally a positioning strategy to move the Hearer in to a place to get the best mutual payoff of $c$. 626 | 627 | In the meta-game, the Speaker acts so that both players can be applicable for the highest possible payoff of $c$. 628 | And a Hearer totally blind to the Speaker's actions should have a bias to the \emph{Surface} scope interpretation strategy. 629 | 630 | If the Hearer or Speaker violate this meta-strategy, they would be subject to a decrease in expected returns over time, independent of the other players actions. 631 | Therefore in a language with the free movement of nominals, we should predict that Hearers should \emph{only} try to interpret sentences in surface order in normal situations, and that speakers should scramble or not depending on which produces a sentence which gives the correct scope interpretations with a surface scope reading. 632 | 633 | All in all, the free availability of a costless movement makes avoiding $-i$ the only possible constraint, meaning that all of the choices the Speaker makes should be assumed to avoid $-i$. 634 | This simply means that surface scope, as the empirical judgments have shown, should be preferred at all times in scrambling languages. 635 | 636 | \subsection{The Generalization} 637 | 638 | We can sum up the generalization of this game theoretic analysis of both English-like and scrambling languages below in (\ref{gen}). 639 | 640 | \begin{exe} 641 | \ex \textbf{Wherever there is free and costless word order, scope ambiguities need not arise, but where word order is inflexible, scope ambiguities occur. 642 | \label{gen}} 643 | \end{exe} 644 | 645 | This generalization simply falls out from the analysis we have outlined, and we can widen the scope and look at other kids of scope ambiguities to see similar effects. 646 | 647 | Before that, just a restatement of the intuitions in intuitive terms. 648 | Hearers assume that sentences with free word-order are always surface scope because, due to the free word-order, the speaker could've put the words in another ideal surface scope reading if such reading had been intended. 649 | On the other hand, in English-like languages, costly transformations are unambiguous because hearers assume that speakers would not have engaged in costly transformations unless they intended the sentence to be in a special surface scope order. 650 | 651 | \emph{But} ambiguity arises in English-like languages when a sentence like ``Everyone loves someone'' is produced. 652 | This is because hearers can say, ``Ah, that may just be the desired reading in surface scope, \emph{or} perhaps it is a suboptimal order, and the speaker didn't want to undergo a costly transformation''. 653 | 654 | Now our initial assumptions have accounted for much variation between different languages, but there is scopal differences \emph{inside} of languages between different constructions that is worth outlining and accounting for in this novel way. 655 | 656 | \section{The Generalization Applied} 657 | 658 | In the Generative Program, part of the common idea of quantifier scope differences between languages has been that there are parametric differences between languages that not only cause syntactic differences, but also these scopal differences. 659 | 660 | One language, due to a syntactic paramter, may have ubiquitous ambiguity due to some parameter setting affecting ``Logical Form'', one might have the reverse. 661 | 662 | I'll argue that this conception is untenable, not just because of the better account we can get from this type of game theoretic and pragmatic model, but also because there are many examples of ``local rigidity'' which, in the same way that English syntactic rigidity produces ambiguity, produce ambiguity only in particular constructions in languages. 663 | Quantifier scope availability, therefore, \emph{cannot} be a language parameter setting, and must be grounded in the very specific context of a construction, as I will show our theory here is. 664 | 665 | \subsection{Flexibility of Negation} 666 | 667 | We can take the generalization in (\ref{gen}) and compare it to the flexibility or rigidity of non-nominal quantificational elements as well. 668 | 669 | English expresses sentential negation in the element \emph{not}. As a descriptive generalization, \emph{not} may occur only after a modal or another auxiliary. In normal discoursive situations, it may not occur after main verbs or before a modal. Many attempts have been made to describe and justify the specifics of these facts. We will not address them here, but assume the empirical facts as given syntactic constraints and proceed. 670 | 671 | On to the scopal facts. Notice first that an English sentence with one modal and one negation produce ambiguity. 672 | 673 | \begin{exe} 674 | \ex Billy can not go. \label{cannot}\hfill ($\neg >$ can; can $> \neg$) 675 | \end{exe} 676 | 677 | (\ref{cannot}) is ambiguous. Negation can take wide scope (which is inverse) such that Billy is \emph{unable} to go, or the modal can take wide (surface) scope, where Billy is able \emph{not} to go, if he so pleases. 678 | 679 | In keeping with our assumptions, we can say that ambiguity arises because the following order in (\ref{badneg}) is syntactically invalid for other reasons in English. 680 | 681 | \begin{exe} 682 | \ex[*]{Billy not can go.\label{badneg}} 683 | \end{exe} 684 | 685 | Since (\ref{badneg}) is syntactically ill-formed, we cannot, by normal syntactic means force negation to linearly scope over the modal, thus its parallel sentence (\ref{cannot}) can be assumed to be a suboptimal enunciation of the meaning of an intended (\ref{badneg}). If we imagine a hypothetical ``negation scrambling'' language where the equivalent of (\ref{badneg}) is available, (\ref{cannot}) should be unambiguously $can > \neg$. 686 | 687 | Now that is the situation of modal and negation scope with one non-main verb. However as inferred previously, where there are multiple auxiliaries, \emph{not} may freely occur after any one. Syntactic flexibility should reduce or eliminate the possibility of ambiguity. This is the case as below. 688 | 689 | \begin{exe} 690 | \ex Billy could not have gone before we arrived.\label{could not} 691 | \ex Billy could have not gone before we arrived.\label{have not} 692 | \end{exe} 693 | 694 | Notice as there is flexibility of negation position with non-modal auxiliaries in English, neither (\ref{could not}) nor (\ref{have not}) are ambiguous. In (\ref{could not}), we express the fact that Billy was unable to go before our arrival. In (\ref{have not}), we express the possibility Billy was able to \emph{not} go, but in a world where Billy did go, (\ref{have not}) may still be true. 695 | No one would utter (\ref{have not}) to mean that the negation takes wider scope when (\ref{could not}), which places the negation more leftward, is a possible alternative. 696 | 697 | %Real world knowledge JR 698 | 699 | Thus even in a single language our generalization holds. 700 | Syntactic rigidity allows for ambiguity, while free flexibility creates situations where ambiguity is ruled out due to the assumption that speakers have that surface scope is universally preferred. 701 | 702 | This is not just true from language to language or construction to construction, but in English, even when specifically addressing negation, \emph{any} highly local syntactic rigidity causes ambiguity and \emph{any} highly local syntactic flexibility disambiguates. 703 | 704 | And as expected, languages that can syntactically bear negation before all modals/verbs, such as Chinese do not create the ambiguity in the rigid English example. 705 | 706 | \begin{exe} 707 | \ex{\gll Shujuan keyi bu gen Guorong {tiao wu}. \parencite[109]{ernst98}\\ 708 | S. may not with G. dance\\ 709 | \trans{``Shujuan may not dance with Guorong.''} \hfill (may $>$ not; *not $>$ may) } 710 | \ex{\gll Shujuan bu keyi gen Guorong {tiao wu}.\\ 711 | S. not may with Guorong dance\\ 712 | \trans{``Shujuan may not dance with Guorong.''} \hfill (not $>$ may; *may $>$ not)} 713 | \end{exe} 714 | 715 | The Persian situation is particularly interesting. In most situations, while noun scrambling is mostly free, scrambling of the verb and its negation is more marked. This manifests in that inverse scope is very possible in positions involving a negation interfacing with another quantifier. 716 | 717 | \begin{exe} 718 | \ex {\gll Yek d\=aneshjui \=an ket\=ab-i-ro na-x\=and. \\ 719 | one student that book-ACC not-read \\ 720 | \trans{``A student didn't read that book.\label{par}''}} 721 | \end{exe} 722 | 723 | As we would predict, (\ref{par}) is ambiguous. It can mean either a certain student didn't read the book ($\exists > \neg$) or that \emph{not one} student read it ($\neg > \exists$). This ambiguity arises because the movement of the verb is more marked. 724 | 725 | In other situations, particularly in movement verbs, the Persian main verb becomes more flexible. SVO order, where the negation is still a pre-verbal clitic, is common with some movement verbs, and as expected, the ambiguity evaporates in (\ref{pm1}) and (\ref{pm2}). 726 | 727 | \begin{exe} 728 | \ex{\gll Billy na-raft hame shahr-i.\\ 729 | B. not-went all city-IND\\ 730 | \trans{``Billy didn't go to every city.'' \hfill ($\neg > \forall$; *$\forall > \neg$)\label{pm1}} 731 | } 732 | \ex{\gll Billy be hame shahr-i na-raft.\\ 733 | B. to all city-IND not-went.\\ 734 | \trans{``Billy didn't go to any city.'' \hfill ($\forall > \neg$; *$\neg > \forall$)\label{pm2}} 735 | } 736 | \end{exe} 737 | 738 | Thus Persian movement verbs, which are uniquely more syntactically mobile show precisely the same scopal effects we predict they should. 739 | 740 | \subsection{Construction-specific Rigidity} 741 | 742 | Since my statement here is that scope ambiguity is merely the result of linear rigidity in syntax, not of some language-wide parameter, we should see the unambiguous surface scope of scrambling languages disappear in particular constructions where normally scramblible nominals are tied in position. 743 | 744 | Chinese, usually a very stablely scrambling or discourse configurational language generally allows the low cost movement of nominals as illustrated in (\ref{chin}). These sentences, as we should expect are unambiguous and force surface scope. In (\ref{chin1}), everyone arrests different women, while in (\ref{chin2}), only one woman, who apparently is a prolific criminal, is arrested. 745 | 746 | \begin{exe} 747 | \ex \begin{xlist}\label{chin} 748 | \ex[]{\gll Meigeren dou zhuazou yige {n\"uren}.\\ 749 | everyone all arrest a woman\\ 750 | \trans{``Everyone arrested a woman.''\label{chin1}} \hfill (${\forall}>{\exists}; *{\exists}>{\forall}$) 751 | } 752 | \ex[]{\gll (You) yige {n\"uren} meigeren dou zhuazou.\\ 753 | (have) a woman everyone all arrest.\\ 754 | \trans{``A woman was arrested by everyone.''\label{chin2}} \hfill (${\exists}>{\forall}; *{\forall}>{\exists}$) 755 | }\end{xlist} 756 | \end{exe} 757 | 758 | However Chinese \emph{bei} pseudo-passives require a particular word order. 759 | They are rigid. 760 | The semantic object is promoted as the initial nominal, while the agent follows the preverbal co-verb ``bei'' as shown in (\ref{chin3}). As (\ref{chin4}) shows, however, the quasi-prepositional \emph{bei} $+$ \emph{agent} constituent may not be fronted or topicalized. 761 | 762 | \begin{exe} 763 | \ex{ \begin{xlist}\label{beis} 764 | \ex[]{\gll Meigeren dou bei yige {n\"uren} zhuazou. \parencite[142]{aoun89}\\ 765 | everyone all PASS a woman arrest\\ 766 | \trans{``Everyone was arrested by a woman.''\label{chin3}} \hfill (${\forall}>{\exists}; {\exists}>{\forall}$) 767 | } 768 | \ex[*]{Bei yige {n\"uren} meigeren dou zhuazou.\\ 769 | PASS a woman everyone all arrest\\ 770 | \label{chin4} 771 | }\end{xlist}} 772 | \end{exe} 773 | 774 | The scopal possibilities follow the predictions perfectly. Since flexible word order is unavailable, (\ref{chin3}) is ambiguous: there can either be one woman arresting everyone, or each person can be arrested by a different woman. 775 | 776 | The intuitions of our game theoretic model in essense propose that (\ref{chin3}) is an ambiguous sentence because its alternative sentence (\ref{chin4}) is not available. 777 | On the other hand, because (\ref{chin1}) \emph{does} have a sensible counterpart (\ref{chin2}) with a different scope order \emph{there is no reason for it to be ambiguous}. 778 | 779 | Interestingly enough, the scope possibilities in Chinese in normal clauses and the \emph{bei} pseudo-passive are precisely the opposite of English, again this falls out from the fact that nominal movement is generally free in Chinese (meaning unambiguous sentences normally) and the additional fact that \emph{bei} passives are not precisely equivalent to their active counterparts, but add additional meaning. 780 | We will discuss this in the next subsection. 781 | 782 | For now it should be noted that the data we've covered from a variety of languages move lockstep together: syntactically rigid constructions exhibit quantifier scope ambiguity, while syntactically flexible constructions do not. 783 | This is not a generalization about the differences between languages, but \emph{inside} languages as well. 784 | 785 | \begin{figure} 786 | \begin{tabular}{ll} 787 | Rigid Constructions & Flexible Constructions \\\hline\hline 788 | English main clauses & Main clauses in scrambling languages \\ 789 | Persian negation & Chinese negation \\ 790 | Typical English negation & English negation around auxes \\ 791 | Chinese passives & English passives*\\ 792 | \textbf{All of these are ambiguous} & \textbf{All of these are non-ambiguous}\\ 793 | \end{tabular} 794 | \caption{Empirical generalizations: Rigidity ${\rightarrow}$ Ambiguity} 795 | \end{figure} 796 | 797 | An approach to scope based in traditional syntax would be able account for the differences \emph{between} languages, saying that the different scope interpretations are built into different syntactic parameters, but as we've shown here, there are scope distinctions \emph{between individual constructions} within a language. 798 | 799 | This along with the fact that each of these differences correlate so well syntactic rigidity or flexibility point to a deeper relationship between scope and syntactic flexibility, a relationship which we have modeled causally above. 800 | 801 | \subsection{Why passivize when you can scramble?\label{passscr}} 802 | 803 | We noted in Section \ref{scbad} that our formal analysis treats the Speaker strategy \textit{Passive} strategy as a \emph{dominated strategy} to \textit{Scramble} in languages where \textit{Scramble} is available. 804 | A decent question for asking is, given our theory, \emph{why indeed} should there exist a passive is one can easily scramble words to a more desired position? Should typical passives exist at all in ``scrambling'' languages? 805 | 806 | First, it's worth saying that this analysis only predicts that scrambling is a superior strategy over passivization for the simple purpose of engineering surface scope order. 807 | There may indeed be other reasons to use a passive in language. 808 | 809 | That said, I think there is a case to be made that indeed scrambling languages rely less on passivization and other transformations. 810 | Or at least, in scrambling languages where passives exist, passives find a distinct semantic or pragmatic niche. 811 | 812 | Take the earlier example of Chinese, a scrambling language\footnote{Or at least a discourse-configurational language. Regardless, a language with relatively free word order. What is important for us is not the cause of the multiple constructions, but the fact that syntactic flexibility is an option.}. 813 | Chinese indeed have a construction sometimes called a ``passive'', and that is the \textit{bei} construction we mentioned in example (\ref{beis}). 814 | Like English passives, Chinese passives promote the object and demote the subject for a different argument structure schema, and a different order. 815 | 816 | However, while the two constructions are similar in form, the Chinese passive has an added meaning: they imply that the action the patient is undergoing is particularly undesired or unfortunate. 817 | That is, while the examples in (\ref{beis}) show the word for ``arrest'', it would be extremely strange to replace that with a non-negative word such as ``praise'', etc. 818 | 819 | While it is not out objective here, it could certainly be argued that while passives may not be the best strategies for getting a desired scope order, these constructions may be put to other purposes or develop special meanings in circumstance. 820 | This could feasibly be done in evolutionary game theory, but that is beyond our purview here. 821 | 822 | Still, implicitly, with the approach to language developed here, languages are bundles of communicative strategies employed for communication. 823 | 824 | \section{Theoretical Issues Solved and Opened} 825 | 826 | \subsection{The Gambit of Linear Order} 827 | 828 | It should be noted that the data of scope present an existential problem for the general interpretation of syntax from a ``logical form'' perspective. On one hand, the assumption has been that scope interpretations are read from quantificational elements which interface with the hierarchical structure of language. This structure (from the Chomskyan perspective) is construed as irrelevant to the linear order of a sentence, which is a later realization of the expression in phonological form. 829 | 830 | But the overwhelming reality of scope as a feature of natural language is that it is manifestly and abundantly tied to linear order, nearly all of the data presented here, along with that in the literature testify to this. 831 | 832 | I think a proper understand of scope would be that \emph{all possible scope readings of all sentences are theoretically possible at all times}. In normal discoursive situations, however, most possible readings as pruned out as implausible, based on pragmatic circumstances or world-knowledge. This also would attest well the conundrum of every syntax class, where graduate students sit around long enough looking at sentences without context and start seeing \emph{all} of the scopal readings after long enough. My analysis here has endeavored to show why some readings are \emph{ruled out} in certain situations, although this is no be-all-end-all solution to scope, precisely because it is a pragmatic, and perhaps extralinguistic portion of language. 833 | 834 | Such a framework would be able to maintain the statement that human language, at its syntactic core, should be independent of linear order, as the linear order effects are part of the pragmatic traits of language use and discourse. 835 | 836 | \subsection{Scope Interpretations are Not Licensed, but \emph{Pruned}} 837 | 838 | Again, I have not crafted a universal account of scope ambiguities, and have deliberately avoid some contradictory examples that I think explicable on other grounds. Take the sentence pair below. 839 | 840 | \begin{exe} 841 | \ex Every boy ate an apple.\label{evboy} 842 | \ex An apple was eaten by every boy.\label{anap} 843 | \end{exe} 844 | 845 | (\ref{evboy}) follows the generalizations we've sketched here in, that it is ambiguous ($\forall>\exists$, $\exists>\forall$). (\ref{anap}), as a passive, is unambiguous, but not in the way we've predicted here, but \emph{only} inverse scope is allowed ($\forall>\exists$, *$\exists>\forall$), or at least, inverse scope is highly preferred. 846 | 847 | 848 | What rules out the surface scope interpretation of (\ref{anap}) is not the pragmatics of passivization \emph{per se}, but the interface of general world knowledge with the inherent telicity of the verb \emph{eat} with a count noun object. The predicate ``ate an apple'' implies that the subject totally consumed an apple, but if the universal quantifier is thought to scope over the existential ``an apple,'' this would have to mean that every boy totally ate the same apple as every other boy, which is logically impossible. 849 | 850 | This makes the otherwise disfavored $\forall>\exists$ interpretation the only logically consistent option. If we rejigger the sentence to remove the telicity, as in (\ref{jig}), we see that the expected scope possibilities return, even when the sentence is still somewhat strange by that interpretation. 851 | 852 | \begin{exe} 853 | \ex Some of an apple was eaten by every boy. \hfill ($\exists>\forall$, $\forall>\exists$)\label{jig} 854 | \end{exe} 855 | 856 | Note \emph{also} that if we imagine (\ref{anap}) in a discourse environment, we're most likely to think of contrastive focus or something else: ``An apple was eaten by every boy, a banana by every woman, a pineapple by every man\ldots'' 857 | 858 | I do \emph{not} consider this a contradiction, but evidence in favor of the wider point. 859 | Scope ambiguities are trimmed away by pragmatic factors. In (\ref{anap}), it is world knowledge, in most of the other examples here, it's economy of derivation. 860 | 861 | \section{Towards a general, game theoretic theory of quantifier scope} 862 | 863 | Our empirical domain established here is quite robust in the data problems we've addressed. 864 | Specifically, we can make predictions about what kinds of languages and constructions make ambiguous scope readings available based on independent factors. 865 | We have looked a number of constructions in a number of languages, but the theory would predict these generalizations will continue to be vindicated. 866 | 867 | Our game theoretic model accounts fairly well for these scopal differences motivated by the availability of different strategies. 868 | I think that this model can be refined substantially in the future, and I plan to do so, but there's some sense in which the intuition is fundamentally ``correct''. 869 | 870 | That said, there are some domains of scope which I have not endeavored to account for due to the more focused scope of the my data here. 871 | Two of these domains are the most prominent: 872 | 873 | \begin{enumerate} 874 | \item The scope differences between universal and existential quantifiers. 875 | \item The scope differences between particular quantifiers of the same ``type'', but generally taking different scope readings. 876 | \end{enumerate} 877 | 878 | It's worth discussing how these problems can be addressed, and how they can be integrated into a general theory of game theoretic quantifier scope we've begun here. 879 | 880 | \subsection{Universal vs. existential quantifiers} 881 | 882 | There have been game theoretic accounts to address these problems, notably in \textcite{clark12}. 883 | Clark models the difference between universal and existential scopes as being an abstract game between falsifier and verifier algorithms. 884 | The scopal differences between universal and existential quantifiers come about from how these two ``players'' proceed to attempt to find a contradiction or vindication of the truth of a sentence in a Model Theoretic framework. 885 | 886 | Based on the linear order of a sentence, we may find a proof or disproof of a sentence in a Model Theoretic world at different times for either existential or universal quantifiers. 887 | Clark's model, although a ``mere'' example in another more general argument, is simple and highly effective at disentangling the scopal tendencies of universal and existential quantifiers. 888 | 889 | There is a possibility of combining this approach with ours into a linearly processed incremental game, where the Hearer weeds out possible interpretations with world knowledge accounted for model theoretically, partially based on cognitive coherence \parencite{langacker87}. 890 | 891 | \subsection{$some$ vs. $a$ vs. $one$; and other scope preferences}\label{prefscope} 892 | 893 | Another domain on which our current theory here is insolvent or at least agnostic is the generally acknowledged tendency for some quantifiers to prefer to take higher or lower scope \parencite{feiman16}. Take the pair of sentences below. 894 | 895 | \begin{exe} 896 | \ex \begin{xlist} 897 | \ex Every girl loves a man. 898 | \ex Every girl loves some man.\label{lessamb} 899 | \end{xlist} 900 | \end{exe} 901 | 902 | Either of these sentences can be interpreted as being ambiguous (${\forall}>{\exists}$ or ${\exists}>{\forall}$), but (\ref{lessamb}) with the quantifier $some$ seems to predispose one to be somewhat closer to the ${\exists}>{\forall}$ interpretation, where every girl loves one particular man, say, Billy. 903 | 904 | We can see a similar effect with universal quantifiers: 905 | 906 | \begin{exe} 907 | \ex \begin{xlist} 908 | \ex Three postmen visited each house.\label{post1} 909 | \ex Three postmen visited every house.\label{post2} 910 | \end{xlist} 911 | \end{exe} 912 | 913 | (\ref{post1}) seems to prefer the (${\exists}>3$) interpretation where at every house there were three, possibly different postmen. 914 | (\ref{post1}) prefers the reading ($3>{\exists}$) where exactly three postmen went to every single house. 915 | 916 | While the account I have built here does quite well to predict the effects of transformations and scrambling on scope interpretations, as well as predicting typological facts, I do not think these narrow differences between the tendencies of particular quantifiers can be captured in our current formalism. 917 | 918 | However, an evolutionary game theoretic account \parencite{maynardsmith73} could do so quite well. 919 | In fact, an evolutionary account could also answer the general question of why languages indeed do have ``synonymous'' quantifiers in the first place. 920 | 921 | Specifically, given what we've modeled here, ambiguity is still a sizeable problem for communication's sake. 922 | To disambiguate sentences which maintain ambiguity, language systems gradually evolve a meta-game or, really \emph{conventions} as to particular quantifiers having particular scope readings. 923 | 924 | That is, in English, for example, $some$ and $a$ may both be existential quantifiers, as $every$ and $each$ are both universal quantifiers, but over time, Schelling Points arise where particular quantifiers are conventionalized as preferring wide or narrow scope. 925 | In English, it seems that both $some$ and $each$ tend to prefer wide scope while $a$ and $every$ prefer narrow scope. 926 | 927 | \subsection{Empirical extensions} 928 | 929 | Even more than formal modeling, I think that our generalization that syntactic rigidity produces scopal ambiguity is an sensible find that could probably be replicated on a much larger scale with many more constructions. 930 | 931 | \section{Closing} 932 | 933 | %Everyone believes that some person loves a dog. 934 | 935 | In closing, much of the confusion about scope can be alleviated by understanding that scope availabilities are determined by pragmatic factors and implicatures that can be modelled game theoretically. We've seen here that the facts about the scope availabilities of most languages fall out quite effortlessly from assumptions about the cost of transformations, the costlessness of scrambling and the wider syntactic capacities of a language. 936 | 937 | I feel that much more work can be note to resolve questions in scope using pragmatic facts, particularly in the areas of telicity and world knowledge. 938 | Additionally, the tools of game theory can prove extremely effective at accounting for scope and other quasi-pragmatic aspects of languages that have traditionally for better or for worse been modeled as parts of or outputs of the formal syntactic engine. 939 | Regardless, there seems to be good circumstantial evidence to lend credence to the idea that scope is not a component of narrow syntax, but a set of extra-UG implicatures we make about language use. 940 | 941 | Additionally, other factors of grammar, such as binding in the classical sense are in need of new life, once insurmountable problems were brought to traditional syntactic analyses of the data. It may be that these other factors, binding, negative polarity items and cross-over effects may actually be derivable on pragmatic grounds, and thus would eliminate such of the theoretical mess and greatly economize and minimize the core language faculty. 942 | 943 | \printbibliography 944 | 945 | \end{document} 946 | -------------------------------------------------------------------------------- /prepurge.tex: -------------------------------------------------------------------------------- 1 | % xelatex 2 | \documentclass{article} 3 | \usepackage[utf8]{inputenc} 4 | \usepackage{ot-tableau} 5 | \usepackage[backend=biber, style=authoryear-icomp]{biblatex} 6 | \usepackage{forest} 7 | \usepackage{tikz} 8 | \usepackage{easylist} 9 | \usepackage{hanging} 10 | \usepackage{hyperref} 11 | \usepackage{blindtext} 12 | \usepackage{tipa} 13 | \usepackage{cgloss4e} 14 | \usepackage{gb4e} 15 | \usepackage{qtree} 16 | \usepackage{enumerate} 17 | \usepackage{longtable} 18 | \usepackage{dialogue} 19 | \usepackage{textgreek} 20 | \usepackage{framed} 21 | \usepackage{amsmath} 22 | \addbibresource{$HOME/Documents/LaTeX/uni.bib} 23 | 24 | \usetikzlibrary{calc} 25 | \usetikzlibrary{matrix} 26 | \usetikzlibrary{positioning} 27 | 28 | 29 | \usetikzlibrary{shapes.geometric, arrows, trees} 30 | 31 | \tikzset{Above/.style={midway,above,font=\scriptsize,text width=1.5cm,align=center,},Below/.style={midway,below,font=\scriptsize,text width=1.5cm,align=center}} 32 | \tikzstyle{box} = [rectangle, centered, draw=black,minimum width=3cm, minimum height=1cm] 33 | \tikzstyle{arrow} = [thick,->,>=stealth] 34 | 35 | 36 | \tikzset{centered/.style=} 37 | 38 | \title{Scope without Syntax: A Game Theoretic Approach} 39 | \author{Luke M. Smith} 40 | 41 | \begin{document} 42 | 43 | \maketitle 44 | 45 | \begin{abstract} 46 | Here I argue that the commonly (and uncommonly) known facts about the availability of quantifier scope interpretations fall out cleanly from communicative constraints which Speakers and Hearers tactically navigate to converge on the intended meaning of an utterance. 47 | This allows a relatively complete and motivated theory of quantifier scope ambiguity wholly without the need to resort to syntactic structure \textit{per se} for the main data. 48 | I model this theory Game Theoretically, in a game where speakers receive a payoff for successful communication, and decrements to payoffs for the use of marked constructions. 49 | These assumptions are sufficient to account for classical scope ambiguity data, but also newly compiled data I present which argues that \emph{word order rigidity}, across languages and constructions is the cause of scope ambiguity. 50 | \end{abstract} 51 | 52 | %\section{Problems with syntactically-derived accounts of scope} 53 | 54 | %\begin{exe} 55 | %\ex 56 | %\begin{xlist} 57 | %\ex Many of the arrows didn't hit the target. 58 | %\ex The target wasn't hit by many of the arrows. 59 | %\end{xlist} 60 | %\end{exe} 61 | 62 | %\begin{exe} 63 | %\ex 64 | %\begin{dialogue} 65 | %\speak{Speaker 1} Look at the target: it wasn't hit by your arrow! 66 | %\speak{Speaker 2} The target wasn't hit by many of the arrows. 67 | %\end{dialogue} 68 | %\end{exe} 69 | 70 | \section{Need for a novel approach to scope} 71 | 72 | I've decided to add this section at the last minute. It will briefly overview some of the problems behind traditional generative attempts at modeling scope, chiefly: 73 | 74 | \begin{itemize} 75 | \item The marked unsystaticity of scope as an indicator of syntactic phenomena, i.e. that there still isn't a commonly accepted metric for what scope effects syntactic movements, etc. should have. 76 | \item The sensitivity of scope to linear order. 77 | \item The ubiquitous ``Chomsky's Aphasia'' in scope judgments and non-categorical judgments. 78 | \end{itemize} 79 | 80 | \section{Assumptions\label{assump}} 81 | 82 | 83 | Before proceeding, I'll make some \emph{a priori} assumptions about scope interpretations. 84 | We will see that much of the diversity of scope can be accounted for merely taking these as interactive assumptions. 85 | 86 | \begin{enumerate} 87 | \item Speakers and listeners prefer for quantifiers to be in ``surface scope'' order. 88 | \item ``Transformations'' classically named (e.g. passives) are ``costly'' or ``dispreferred'' in some sense. 89 | \item ``Scrambling'' in languages which exhibit it, is not similarly costly. 90 | \end{enumerate} 91 | 92 | Before explaning the model, it's at least worth justifying all three of these on functional grounds. 93 | 94 | \subsection{Preference for Surface Scope} 95 | 96 | <++> 97 | 98 | \subsection{Transformations are ``marked''} 99 | 100 | A longstanding assumption of transformational grammar was that those utterances which are ``transformed'' are in some ways, more marked or at least are derived from simplex expressions. 101 | 102 | \begin{exe} 103 | \ex\label{caes} 104 | \begin{xlist} 105 | \ex Caesar crossed the Rubicon.\label{simp} 106 | \ex It was Caesar who crossed the Rubicon.\label{celft} 107 | \ex The Rubicon was crossed by Caesar.\label{pass} 108 | \end{xlist} 109 | \end{exe} 110 | 111 | That is, while all sentences in (\ref{caes}) share a semantically equivalent kernel, (\ref{simp}) is in someway more basic than the cleft (\ref{celft}) or the passive (\ref{pass}). 112 | Earlier ideas in Generative Grammar assumed that this was because (\ref{celft}) and (\ref{pass}) were literally derived from (\ref{simp}), thus leading to the psycholinguistic thesis of the Derivational Theory of Complexity, hypothesizing that the latter two sentences were marked 113 | 114 | Theories such as this have fallen out of favor in mainstream Generative Grammar, but regardless, data from acquisition does indeed show that sentences such as (\ref{celft}) and (\ref{pass}) are acquired and employed at a distinctly later stage of language development. 115 | 116 | 117 | \subsection{Scrambling is not costly} 118 | 119 | This may fall out for free depending on one's account of the costliness of transformations. 120 | For example, if we say that the passive is generally disprefered because it consists in adding additional morphemes and words to a clause, we implicitly say that scrambled sentences, since they require no additional morphology or periphrasis, are not similarly costly. 121 | 122 | \section{Basic English Data and Passives\label{eng}} 123 | 124 | With the background established, we can move to address data and spelling out this model. 125 | First note some rudimentary scope facts in English. 126 | Generally, unmarked active ``kernel'' sentences like (\ref{evman}) and (\ref{evsp}) demonstrate fairly robust scope ambiguity. 127 | Thus, (\ref{evman}) can mean either that there is one particular girl that every man saw ($\exists>\forall$) or that each man saw a (potentially different) girl ($\forall>\exists$). 128 | 129 | \begin{exe} 130 | \ex\label{first}{\begin{xlist} 131 | \ex Every man saw a girl. \hfill ($\forall > \exists$; $\exists > \forall$)\label{evman} 132 | \ex Everyone speaks two languages. \hfill ($\forall > 2$; $2 > \forall$)\label{evsp} 133 | \end{xlist}} 134 | \ex{\begin{xlist} 135 | \ex A girl was seen by every man. \hfill ($\exists > \forall$; *$\forall > \exists$)\label{agirl} 136 | \ex Two languages are spoken by everyone. \hfill ($2 > \forall$; *$\forall > 2$)\label{2lang} 137 | \end{xlist}} 138 | \end{exe} 139 | 140 | In the ``transformed'' passive equivalents of the two sentences, however, syntactic ambiguity becomes unavailable and surface scope is mandatory. 141 | Thus (\ref{agirl}) is only true if there was only one girl in question, while (\ref{2lang}) is only true if all of the people speak the same two particular languages. 142 | We see that this scopal alternation generally holds across most active/passive sentence pairs.\footnote{Some exceptions will be discussed later.} 143 | 144 | \begin{exe} 145 | \ex{\begin{xlist} 146 | \ex A man ate every watermelon. \hfill ($\exists>\forall$; $\forall>\exists$) 147 | \ex Every watermelon was eaten by a man.\label{passman} \hfill ($\forall>\exists$; *$\exists>\forall$) 148 | \end{xlist}} 149 | \ex{\begin{xlist}\label{love} 150 | \ex Everyone loves someone. \hfill ($\forall>\exists$; $\exists>\forall$)\label{sent} 151 | \ex Someone is loved by everyone.\label{passsome} \hfill ($\exists>\forall$; *$\forall>\exists$) 152 | \end{xlist}} 153 | \end{exe} 154 | 155 | It should be said that while (\ref{passman}) and (\ref{passsome}) are labeled as requiring surface scope, there are indeed situations where the inverse readings are possible or required. 156 | While when some traditional accounts of scope categorically rule these sentences out, for me, what is important is that the inverse passive readings are simply \emph{highly dispreferred}. 157 | As our analysis will show, there is nothing formally syntactic that makes these sentences essentially bad, but merely the results of the Game Theoretic analysis. 158 | The important fact here is merely that English passives, without other context strongly imply only surface scope. 159 | 160 | 161 | \section{Model} 162 | 163 | Additionally, it's important to be clear about the Game Theoretics of communication. 164 | Resolving scope ambiguities like that in (\ref{first}) is a kind of coordination game with imperfect information. 165 | That is, two interlocutors must converge on the same interpretation of a sentence which has been decided by circumstance; 166 | the Speaker knows the required interpretation and in speaking attempts to signal it to the Hearer. 167 | Both players ``win'' if the Speaker is succesful in leading the Hearer to the correct interpretation. 168 | If the speaker intends for a universal quantifier, such as \emph{every}, to scope over an existential one, such as \emph{some}, he ideally must word his sentence in such a way to communicate this. 169 | 170 | \begin{framed} 171 | \small 172 | 173 | \textbf{Game Theoretic Terms} 174 | 175 | \textbf{Imperfect information} -- When at least one player is not perfectly aware of the actions of another. In our game, the Hearer is not aware of the decision of Nature, ergo this is a game with imperfect information. 176 | 177 | \textbf{Incomplete information} -- When at least one player is not aware of the payoffs for a player. Although this concept is frequently confused with imperfect information, we \emph{do not} have a incomplete information game. 178 | 179 | \textbf{Signalling} -- When a player voluntarily undergoes a costs to communicate his tactics or strength. For example, a zebra, noticing a stalking lion may ``irrationally'' jump up and down in place instead of running to show his spriness and tell the lion he isn't an easy target. 180 | 181 | \textbf{Nash Equilibrium} -- A point in a game where no player can improve his position by changing strategies given what he knows. While Nash Equilibria are usually the McGuffin of Game Theoretic analysis, our game has no proper Nash Equilibrium (not assuming iteration). 182 | 183 | \textbf{Schelling Point} -- A point which is not a Nash Equilibrium, but due to some meta-game reasoning is a particularly marked. 184 | \end{framed} 185 | 186 | 187 | \begin{figure} 188 | \begin{center} 189 | \begin{tikzpicture}[node distance=2cm] 190 | 191 | \node (nature) [box, align=center] {{\large \textbf{ Player 0: ``Nature''}}\\Determines desired quantifier scope interpretation $s$}; 192 | \node (speaker) [box, align=center, below of=nature] {{\large \textbf{Player 1: ``Speaker''}}\\Determines a best wording $w$ to communicate $s$ }; 193 | \node (hearer) [box, align=center, below of=speaker] {{\large \textbf{Player 2: ``Hearer''}}\\Must guess $s$ based $w$}; 194 | 195 | \draw [arrow] (nature) -- (speaker) ; 196 | \draw [arrow] (speaker) -- (hearer) ; 197 | \end{tikzpicture} 198 | \end{center} 199 | \caption{The sequence of player choices\label{seq}} 200 | \end{figure} 201 | 202 | To be more specific, we can say this is a kind of 3-player coordination game (where the sequence is indicated in Figure \ref{seq}). 203 | Player 0, who we can term \textbf{Nature} dictates what the needed scope interpretation should be, that is, whether, based on circumstances, a subject quantifier must scope over an object quantifier, or \emph{vice versa} or any other combination of quantificational elements. 204 | \footnote{We will only be including subject and object quantification for sake of simplicity to outline some general principles.} 205 | We can think of the choice of Player 0, Nature, as a random or given element of the model. 206 | Player 1, \textbf{the Speaker}, knows what the needed scope given by Nature is, and has to encode a linguistic message to communicate it to Player 2: \textbf{the Hearer} who is ignorant of it (illustrated in Figure \ref{tree}). 207 | In each language, the Speaker might have different strategies usable to communicate this message, depending on the structure of a language. 208 | \footnote{Thus, our intent here is not to argue how or why a given sentence in a language is grammatical or acceptable, but why Speakers choose to use a given sentence to communicate a particular scope reading.} 209 | 210 | If the Hearer's interpreted scope and the scope selected by Nature match, both human players get a payoff (represented as $c$ for \emph{\textbf{c}ommunication}), while if they do not match, there has been a miscommunication and this there is no payoff. 211 | Similarly, we can formalize our assumptions in the Section \ref{assump}. 212 | If transformations, specifically passives, are costly or dispreferred in some way, we can model them as saying that they reduce the payoff to the speaker to some degree (designated by $-p$). 213 | Similarly, instances of free word order and so-called ``scrambling'' do \emph{not} reduce any payoff. 214 | Lastly, surface scope should be universally preferred, so in situations where a speaker and hearer settle on an \emph{inverse} scope reading of a sentence, their payoffs are reduced by some degree (symbolized by $-i$). 215 | 216 | We should also assume that $c > (p + i)$, meaning that it is always preferable for the two interlocutors to understand each other even if transformations and inverse scope may dig into that payoff. 217 | Also, $p$ and $i$ are not necessarily larger or smaller than one another, and may vary from situation to situation, meaning that in some situations, it may be preferable for a speaker to vie for inverse scope rather than performing a transformation, while in others, it opposite may be true. 218 | 219 | The particulars of an instantiation of the game are based in the structure of whatever language is being spoken. 220 | For any given language, there will be a different set of syntactically valid utterances that the Speaker can use to signal to the Hearer what the intended scope is. 221 | Given the constraints posited above, we will assume that surface scope is the ideal, but different languages differ in their abilities to use different transformations or scrambling. 222 | 223 | 224 | \subsection{The Game Theoretic Core} 225 | 226 | Regardless, given our constraints above, we can derive these facts of the difference between actives and passives from the interaction of strategic interpretation on the part of the two interlocutors. 227 | Assume the three player game above (of Nature, a Speaker and a Hearer), dealing with the kernel sentence in (\ref{sent}) ``Everyone loves someone,'' depicted in the decision tree in Figure \ref{tree}. 228 | 229 | First, the Nature player determines whether the intended scope of the utterance should be where the universal quantifier takes wide scope ($\forall>\exists$, or $Sub > Obj$) or where the existential does ($\exists>\forall$, or $Obj > Sub$). 230 | Then the Speaker, aware of Nature's choice, takes his turn choosing either to word the sentence as the active ``Everyone loves someone'' or the passive ``Someone is loved by everyone''. 231 | Lastly, the Hearer, unaware of Nature's original decision, chooses whether to interpret the sentences with surface scope or inverse scope. 232 | 233 | To repeat, if the Hearer guesses the correct scope as defined by Nature, both the Speaker and Hearer receive a payoff of $c$. 234 | If the players fail to engineer this, both will receive no payoff. 235 | Additionally, because a passive transformation is ``costly,'' the payoff of the Speaker will be deducted by $p$ whenever he chooses to produce a passive. 236 | Lastly, if the dispreferred inverse scope has to be employed, both speakers will have a penalty of $i$. 237 | 238 | \begin{figure} 239 | \begin{center} 240 | % First, set the overall layout of the tree 241 | % You might need to play with these sizes to ensure nothing overlaps. 242 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 243 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 244 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 245 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 246 | \begin{tikzpicture} 247 | %Start with the parent node, and slowly build out the tree 248 | % with each "child" representing a new level of the diagram 249 | % each "node" represents a labelled (or unlabeled if you 250 | % want) node in the diagram. 251 | \node {Nature} 252 | child{ 253 | node{Speaker} 254 | child{ 255 | node(d){Hearer} 256 | child{ 257 | node{$\displaystyle\binom{c}{c}$} 258 | edge from parent 259 | node[left]{S} 260 | } 261 | child{ 262 | node{$\displaystyle\binom{-i}{-i}$} 263 | edge from parent 264 | node[right]{I} 265 | } 266 | edge from parent 267 | node[left]{A} 268 | } 269 | child{ 270 | node(a){Hearer} 271 | child{ 272 | node{$\displaystyle\binom{-p}{0}$} 273 | edge from parent 274 | node[left]{S} 275 | } 276 | child{ 277 | node{$\displaystyle\binom{c-p-i}{c-i}$} 278 | edge from parent 279 | node[right]{I} 280 | } 281 | edge from parent 282 | node[right]{P} 283 | } 284 | edge from parent 285 | node[left]{${\forall}>{\exists}$} 286 | } 287 | child{ 288 | node{Speaker} 289 | child{ 290 | node(b){Hearer} 291 | child{ 292 | node{$\displaystyle\binom{0}{0}$} 293 | edge from parent 294 | node[left]{S} 295 | } 296 | child{ 297 | node{$\displaystyle\binom{c-i}{c-i}$} 298 | edge from parent 299 | node[right]{I} 300 | } 301 | edge from parent 302 | node[left]{A} 303 | } 304 | child{ 305 | node(c){Hearer} 306 | child{ 307 | node{$\displaystyle\binom{c-p}{c}$} 308 | edge from parent 309 | node[left]{S} 310 | } 311 | child{ 312 | node{$\displaystyle\binom{-p-i}{-i}$} 313 | edge from parent 314 | node[right]{I} 315 | } 316 | edge from parent 317 | node[right]{P} 318 | } 319 | edge from parent 320 | node[right]{${\exists}>{\forall}$} 321 | }; 322 | \draw [dashed](d)to[in=180](b); 323 | \draw [dashed](a)to[in=180](c); 324 | \end{tikzpicture} 325 | \end{center} 326 | \caption{The Extensive Game} 327 | asdfkjhasdkjfh 328 | 329 | asdf 330 | \end{figure} 331 | 332 | %\begin{figure} 333 | % 334 | %\begin{forest} 335 | %for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 336 | %(.child anchor)\forestoption{edge label}; 337 | %}, 338 | %l sep=2cm, 339 | %} 340 | %[Nature,rectangle, s sep=25pt, 341 | %[Speaker,edge label={node[Below]{$\exists>\forall$}} 342 | %[Hearer,edge label={node[Below]{Passive}} 343 | %[{$-p-i,-i$},edge label={node[Below]{Inverse}}] 344 | %[{$c-p,x$},edge label={node[Below]{Surface}}] 345 | %] 346 | %[Hearer,edge label={node[Above]{Active}} 347 | %[{$c-i,c-i$},edge label={node[Below]{Inverse}}] 348 | %[{$0,0$},edge label={node[Below]{Surface}}] 349 | %] 350 | %] 351 | %[Speaker,edge label={node[Above]{$\forall>\exists$}} 352 | %[Hearer,edge label={node[Below]{Passive}} 353 | %[{$c-p-i,c-i$},edge label={node[Below]{Inverse}}] 354 | %[{$-p,0$},edge label={node[Below]{Surface}}] 355 | %] 356 | %[Hearer,edge label={node[Above]{Active}} 357 | %[{$-i,-i$},edge label={node[Below]{Inverse}}] 358 | %[{$c,c$},edge label={node[Below]{Surface}}] 359 | %] 360 | %] 361 | %] 362 | %\end{forest} 363 | % 364 | %\caption{Decision Flow of the Game of ``Everybody loves somebody''\label{tree}} 365 | %\end{figure} 366 | 367 | 368 | Since this decision tree involves three players with substantive choices, it helps to narrow down the decision to find Nash Equilibria or optimal strategies. 369 | Let's put ourselves in the position of the Hearer. 370 | The Hearer is the one dealing with the informational asymmetry guessing the choice of Nature given the Speaker's utterance. 371 | Given the aforementioned decision tree in Figure \ref{tree}, the Hearer can make two hypotheses about Nature, that it chose to demand that the subject $\forall$ scope over the object $\exists$, which is represented in Figure \ref{all}, or that it demands that the object $\exists$ should scope over the subject $\forall$. 372 | 373 | %\begin{figure} 374 | %\centering 375 | %\begin{tikzpicture} 376 | %\matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 377 | %$c$&$-p$\\ 378 | %$c$&$0$\\ 379 | %$-i$&$c-p-i$\\ 380 | %$-i$&$c-i$\\ 381 | %}; 382 | %\draw (m.north east) rectangle (m.south west); 383 | %\draw (m.north) -- (m.south); 384 | %\draw (m.east) -- (m.west); 385 | % 386 | %\coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 387 | %\coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 388 | %\node[above=5pt of a,anchor=base] {Active}; 389 | %\node[above=5pt of b,anchor=base] {Passive}; 390 | % 391 | %\coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 392 | %\coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 393 | %\node[left=2pt of c,text width=1cm] {Surface}; 394 | %\node[left=2pt of d,text width=1cm] {Inverse}; 395 | % 396 | %\node[above=18pt of m.north] (firm b) {Speaker}; 397 | %\node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 398 | % 399 | %%\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$}; 400 | %\end{tikzpicture} 401 | %\caption{If Nature selects $\forall>\exists$\label{all}} 402 | %\end{figure} 403 | 404 | The key to the strategy is the cost of the passive $p$. 405 | Let's take the situation when Nature selects ${\forall}>{\exists}$. 406 | In that case, the hypothetical active form ``Everybody loves someone'' already has the correct surface scope order. 407 | While it is not immediately sure that the Hearer would determine that this active clause is indeed the required order, it costs the Speaker neither decrements of $p$ or $i$. 408 | 409 | If the Speaker were to passivize the sentence to ``Someone is loved by everybody'', not only would he be incurring the loss of $p$ for the passive transformation, but if the Hearer did guess correctly that the sentences should have \emph{inverse} scope in this reading, both players would additionally be losing $i$. 410 | 411 | The Speaker therefore is in a position of two theoretically uncertain outcomes, one that can yield him $c$, while the other can yield him only $c-p-i$. 412 | All things considered, $c$ is preferrable, and therefore using the active sentence to express ${\forall}>{\exists}$ should be preferrable. 413 | While this is not a proper Nash Equilibrium, since we are dealing with a non-simultaenous game, this decision can act as a \emph{signal} to the second player, the Hearer. 414 | 415 | The Hearer, knowing that there is this Schelling Point for choosing the active sentence when given ${\forall}>{\exists}$ can therefore conclude by deduction that if the Speaker for some reason chooses to word his sentence in the passive, it is nearly certain that Nature meant \emph{the other} alternative: ${\exists}>{\forall}$. 416 | Or put more generally in (\ref{cost}). 417 | 418 | \begin{exe} 419 | \ex{\textit{A speaker will not engage in a costly transformation which yields an undesired scope order.\label{cost}}} 420 | \end{exe} 421 | 422 | \begin{figure} 423 | \centering 424 | \begin{tikzpicture} 425 | 426 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 427 | $0$&$c-p$\\ 428 | $0$&$c$\\ 429 | $c-i$&$-p-i$\\ 430 | $c-i$&$-i$\\ 431 | }; 432 | \draw (m.north east) rectangle (m.south west); 433 | \draw (m.north) -- (m.south); 434 | \draw (m.east) -- (m.west); 435 | 436 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 437 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 438 | \node[above=5pt of a,anchor=base] {Active}; 439 | \node[above=5pt of b,anchor=base] {Passive}; 440 | 441 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 442 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 443 | \node[left=2pt of c,text width=1cm] {Surface}; 444 | \node[left=2pt of d,text width=1cm] {Inverse}; 445 | 446 | \node[above=18pt of m.north] (firm b) {Speaker}; 447 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 448 | 449 | %\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$}; 450 | \end{tikzpicture} 451 | \caption{If Nature selects $\exists>\forall$\label{some}} 452 | \end{figure} 453 | 454 | 455 | %Figure \ref{some} gives a Hearer no conclusion about the Speaker's dominant strategy, it is simply a kind of \emph{Matching Pennies} game with the additional cost of the passive transformation.\footnote{There is the clear \emph{focal point} of the Speaker using an \emph{Active} and the Hearer interpreting inverse scope, but this is illusory given the random element of Nature and the wider tree in Figure \ref{tree}.} However, since we cannot \emph{rule out} the use of the passive, and we have already established (\ref{cost}), we can also logically conclude (\ref{pass}). 456 | Or to spell (\ref{cost}) out more specifically in our context, see (\ref{passa}). 457 | 458 | 459 | \begin{exe} 460 | \ex{\textit{The use of a costly reordering transformation, \emph{ceteris paribus}, entails that the underlying object should take wide scope over the subject. Or put another way, scopal ambiguity dissappears in favor of surface scope after a costly transformation.\label{passa}}} 461 | \end{exe} 462 | 463 | To put it in more intuitive terms, if the subject does something costly like passivization to a sentence, \emph{he is doing it for a reason}, specifically here to avoid the other loss of $i$. 464 | Passivizing only to also lose $i$ is not a good Schelling Point strategy. 465 | For this reason, in most pragmatic circumstances, passivized sentences appear as unambiguous, seeing that we conclude that they are motivated to avoid the cost of the inverse scope. 466 | 467 | In the situation where Nature chooses ${\exists}>{\forall}$, the situation is less clear. 468 | This is because the Speaker has two possible winning payoffs: $c-i$ and $c-p$, neither of which is necessarily preferrable since we have not established whether $p>i$, nor do I think one is always larger than the other. 469 | In this situation, a Speaker could passivize and to avoid inverse scope order, or bite the bullet and take inverse scope without the passivization, both with uncertainty. 470 | The end result is that the active sentence ``Everyone loves someone'' does not clearly communicate whether Nature choose ${\forall}>{\exists}$ or ${\exists}>{\forall}$ since there is no obvious Schelling Point to rule out one of the strategies. Therfore, while the English passive is unambiguous due to the presence of a Schelling Point, the English active is not. 471 | 472 | \subsection{Scrambling\label{scramb}} 473 | 474 | But how should scope ambiguities work where there are ``costless'' ways of reordering quantified nominals? Scrambling languages present ways of reordering nominals without a marked transformation. In our model, Speakers in languages like this, such as German, Persian, Korean and Japanese, have access to another strategy aside from producing an active or passive clause. They may also \emph{scramble} the object such that it appears to the left of the subject. 475 | 476 | First a theoretical note. 477 | The ``scrambling'' tendencies of each of these languages may be different: German ``scrambling'' is quite different syntactically than Korean's, etc. 478 | This is not so important to us here. 479 | We only need to know if there is a valid reordering strategy in a language which is not marked in the way that passives are. 480 | Why German or Perian or other languages vary with respect to syntactic flexibility is not germane for us here, only the \emph{effects} of these traits on scopal possibilities. 481 | 482 | \subsubsection{Scope in Scrambling Languages} 483 | 484 | First the empirical facts. 485 | German, a scrambling language shows a very different paradigm of scope availabilities than does English. 486 | Even in ``kernel'' sentences like (\ref{g}), surface scope is the only plausible interpretation. 487 | The same is true in the scrambled sentence (\ref{gs}), where the object has been scrambled left of the subject. 488 | 489 | \begin{exe} 490 | \ex{\gll dass eine Frau jeden liebt\\ 491 | that a woman everybody loves\\ 492 | \trans{``\ldots that everyone loves a woman\label{g}''\hfill (some $>$ every; ??every $>$ some)}} 493 | \ex{\gll dass jeden eine Frau liebt\\ 494 | that everybody a woman loves\\ 495 | \trans{``\ldots that everyone loves a woman\label{gs}'' \hfill (every $>$ some; ??some $>$ every)}} 496 | \end{exe} 497 | 498 | This universal surface scope is well mirrored in other languages. 499 | \textcite{karimi03} notes that one of the principle differences between scrambling languages and ones with inflexible word order like English is the lack of ambiguity. 500 | We can see similar patterns in Persian in (\ref{pers}). 501 | 502 | \begin{exe} 503 | \ex\label{pers} \begin{xlist} 504 | \ex {\gll Yek d\=aneshju hame ket\=ab-i x\=and. \\ 505 | a student all book-IND read \\ 506 | \trans{``A student read every book.''\hfill ($\exists > \forall$; *$\forall > \exists$)}} 507 | \ex {\gll Hame ket\=ab-i yek d\=aneshju x\=and. \\ 508 | all book-IND a student read \\ 509 | \trans{``A student read every book.''\hfill ($\forall > \exists$; *$\exists > \forall$)}} 510 | \end{xlist}\end{exe} 511 | 512 | 513 | \subsubsection{An Account of Scramblible Scope} 514 | 515 | In our Game Theoretic framework, we can say that the \emph{Scramble} strategy, which consists of moving the object left of the subject, achieves the linear order of passivization without the cost of $p$ to the Speaker. 516 | Because of this, \emph{Scramble} in a scrambling language is always preferable to the dominated strategy \emph{Passive} for the Speaker. 517 | 518 | \begin{figure} 519 | 520 | \begin{forest} 521 | for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 522 | (.child anchor)\forestoption{edge label}; 523 | }, 524 | l sep=2cm, 525 | } 526 | [Nature,rectangle, s sep=25pt, 527 | [Speaker,edge label={node[Below]{$\exists>\forall$}} 528 | [Hearer,edge label={node[Below]{Passive}} 529 | [{$-p-i,-i$},edge label={node[Below]{Inverse}}] 530 | [{$c-p,c$},edge label={node[Below]{Surface}}] 531 | ] 532 | [Hearer,edge label={node[Above]{Active}} 533 | [{$c-i,c-i$},edge label={node[Below]{Inverse}}] 534 | [{$0,0$},edge label={node[Below]{Surface}}] 535 | ] 536 | [Hearer, edge label={node[Above]{Scramble}} 537 | [{$-i,-i$}, edge label={node[Below]{Inverse}}] 538 | [{$c,c$}, edge label={node[Below]{Surface}}] 539 | ] 540 | ] 541 | [Speaker,edge label={node[Above]{$\forall>\exists$}} 542 | [Hearer,edge label={node[Below]{Passive}} 543 | [{$c-p-i,c-i$},edge label={node[Below]{Inverse}}] 544 | [{$-p,0$},edge label={node[Below]{Surface}}] 545 | ] 546 | [Hearer,edge label={node[Above]{Active}} 547 | [{$-i,-i$},edge label={node[Below]{Inverse}}] 548 | [{$c,c$},edge label={node[Below]{Surface}}] 549 | ] 550 | [Hearer, edge label={node[Above]{Scramble}} 551 | [{$c-i$}, edge label={node[Below]{Inverse}}] 552 | [{$0,0$}, edge label={node[Below]{Surface}}] 553 | ] 554 | ] 555 | ] 556 | \end{forest} 557 | 558 | \caption{Decision Flow of the Game of ``Everybody loves somebody'' in a Scrambling Language\label{trees}} 559 | \end{figure} 560 | 561 | Thus if we disregard the possibility of passivization as dispreferred as a scope technique, once again, both human players have two possible choices. 562 | Once again, we can again simplify the decision tree into two two-dimensional grids given the two different possible choices of the Nature player. 563 | We should see that there is no straight-forward dominant strategy for either player, but a very obvious signalling opportunity arises in the meta-game, or a Schelling Point. 564 | 565 | 566 | \begin{figure} 567 | \centering 568 | \begin{tikzpicture} 569 | 570 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 571 | $c$&$0$\\ 572 | $c$&$0$\\ 573 | $-i$&$c-i$\\ 574 | $-i$&$c-i$\\ 575 | }; 576 | \draw (m.north east) rectangle (m.south west); 577 | \draw (m.north) -- (m.south); 578 | \draw (m.east) -- (m.west); 579 | 580 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 581 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 582 | \node[above=5pt of a,anchor=base] {Active}; 583 | \node[above=5pt of b,anchor=base] {Scramble}; 584 | 585 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 586 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 587 | \node[left=2pt of c,text width=1cm] {Surface}; 588 | \node[left=2pt of d,text width=1cm] {Inverse}; 589 | 590 | \node[above=18pt of m.north] (firm b) {Speaker}; 591 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 592 | 593 | %\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$ in a scrambling langugae}; 594 | \end{tikzpicture} 595 | \caption{If Nature selects $\forall>\exists$ in a scrambling language\label{2s1}} 596 | \end{figure} 597 | 598 | 599 | \begin{figure} 600 | \centering 601 | \begin{tikzpicture} 602 | 603 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 604 | $0$&$c$\\ 605 | $0$&$c$\\ 606 | $c-i$&$-i$\\ 607 | $c-i$&$-i$\\ 608 | }; 609 | \draw (m.north east) rectangle (m.south west); 610 | \draw (m.north) -- (m.south); 611 | \draw (m.east) -- (m.west); 612 | 613 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 614 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 615 | \node[above=5pt of a,anchor=base] {Active}; 616 | \node[above=5pt of b,anchor=base] {Scramble}; 617 | 618 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 619 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 620 | \node[left=2pt of c,text width=1cm] {Surface}; 621 | \node[left=2pt of d,text width=1cm] {Inverse}; 622 | 623 | \node[above=18pt of m.north] (firm b) {Speaker}; 624 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 625 | 626 | %\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$}; 627 | \end{tikzpicture} 628 | \caption{If Nature selects $\exists>\forall$ in a scrambling language\label{2s2}} 629 | \end{figure} 630 | 631 | Specifically, independent of the Speaker and Nature's choices, the Hearer will want to avoid choosing the \emph{Inverse} strategy. 632 | The Speaker realizes this and can strategically select his strategy based on what will require the Hearer to \emph{not} select the \emph{Inverse} strategy. 633 | This acts as a signal to the Hearer. 634 | 635 | In the meta-game, the Speaker acts so that both players can be applicable for the highest possible payoff of $c$. 636 | And a Hearer totally blind to the Speaker's actions should have a bias to the \emph{Surface} scope interpretation strategy. 637 | 638 | If the Hearer or Speaker violate this meta-strategy, they would be subject to a decrease in expected returns over time, independent of the other players actions. 639 | Therefore in a language with the free movement of nominals, we should predict that Hearers should \emph{only} try to interpret sentences in surface order in normal situations, and that speakers should scramble or not depending on which produces a sentence which gives the correct scope interpretations with a surface scope reading. 640 | 641 | All in all, the free availability of a costless movement makes avoiding $-i$ the only possible constraint, meaning that all of the choices the Speaker makes should be assumed to avoid $-i$. 642 | This simply means that surface scope, as the empirical judgments have shown, should be preferred at all times in scrambling languages. 643 | 644 | \subsection{The Generalization} 645 | 646 | We can sum up the generalization of this Game Theoretic analysis of both English-like and scrambling languages below in (\ref{gen}). 647 | 648 | \begin{exe} 649 | \ex \textbf{Wherever there is free and costless word order, scope ambiguities need not arise, but where word order is inflexible, scope ambiguities occur. 650 | \label{gen}} 651 | \end{exe} 652 | 653 | This generalization simply falls out from the analysis we have outlined, and we can widen the scope and look at other kids of scope ambiguities to see similar effects. 654 | 655 | Before that, just a restatement of the intuitions in intuitive terms. 656 | Hearers assume that sentences with free word-order are always surface scope because, due to the free word-order, the speaker could've put the words in another ideal surface scope reading if such reading had been intended. 657 | On the other hand, in English-like languages, costly transformations are unambiguous because hearers assume that speakers would not have engaged in costly transformations unless they intended the sentence to be in a special surface scope order. 658 | 659 | \emph{But} ambiguity arises in English-like languages when a sentence like ``Everyone loves someone'' is produced. 660 | This is because hearers can say, ``Ah, that may just be the desired reading in surface scope, \emph{or} perhaps it is a suboptimal order, and the speaker didn't want to undergo a costly transformation''. 661 | 662 | Now our initial assumptions have accounted for much variation between different languages, but there is scopal differences \emph{inside} of languages between different constructions that is worth outlining and accounting for in this novel way. 663 | 664 | \subsection{Intra- vs. Inter-language variation} 665 | 666 | In the Generative Program, part of the common idea of quantifier scope differences between languages has been that there are parametric differences between languages that not only cause syntactic differences, but also these scopal differences. 667 | 668 | One language, due to a scopal paramter, may have ubiquitous ambiguity due to some parameter setting affecting ``Logical Form'', one might have the reverse. 669 | 670 | I'll argue that this conception is untenable, not just because of the better account we can get from this type of Game Theoretic and pragmatic model, but also because there are many examples of ``local rigidity'' which, in the same way that English syntactic rigidity produces ambiguity, produce ambiguity only in particular constructions in languages. 671 | Quantifier scope availability, therefore, \emph{cannot} be a language parameter setting, and must be grounded in the very specific context of a construction, as I will show our theory here is. 672 | 673 | \subsubsection{Flexibility of Negation} 674 | 675 | We can take the generalization in (\ref{gen}) and compare it to the flexibility or rigidity of non-nominal quantificational elements as well. 676 | 677 | English expresses sentential negation in the element \emph{not}. As a descriptive generalization, \emph{not} may occur only after a modal or another auxiliary. In normal discoursive situations, it may not occur after main verbs or before a modal. Many attempts have been made to describe and justify the specifics of these facts. We will not address them here, but assume the empirical facts as given syntactic constraints and proceed. 678 | 679 | On to the scopal facts. Notice first that an English sentence with one modal and one negation produce ambiguity. 680 | 681 | \begin{exe} 682 | \ex Billy can not go. \label{cannot}\hfill ($\neg >$ can; can $> \neg$) 683 | \end{exe} 684 | 685 | (\ref{cannot}) is ambiguous. Negation can take wide scope (which is inverse) such that Billy is \emph{unable} to go, or the modal can take wide (surface) scope, where Billy is able \emph{not} to go, if he so pleases. 686 | 687 | In keeping with our assumptions, we can say that ambiguity arises because the following order in (\ref{badneg}) is syntactically invalid for other reasons in English. 688 | 689 | \begin{exe} 690 | \ex[*]{Billy not can go.\label{badneg}} 691 | \end{exe} 692 | 693 | Since (\ref{badneg}) is syntactically ill-formed, we cannot, by normal syntactic means force negation to linearly scope over the modal, thus its parallel sentence (\ref{cannot}) can be assumed to be a suboptimal enunciation of the meaning of an intended (\ref{badneg}). If we imagine a hypothetical ``negation scrambling'' language where the equivalent of (\ref{badneg}) is available, (\ref{cannot}) should be unambiguously $can > \neg$. 694 | 695 | Now that is the situation of modal and negation scope with one non-main verb. However as inferred previously, where there are multiple auxiliaries, \emph{not} may freely occur after any one. Syntactic flexibility should reduce or eliminate the possibility of ambiguity. This is the case as below. 696 | 697 | \begin{exe} 698 | \ex Billy could not have gone before we arrived.\label{could not} 699 | \ex Billy could have not gone before we arrived.\label{have not} 700 | \end{exe} 701 | 702 | Notice as there is flexibility of negation position with non-modal auxiliaries in English, neither (\ref{could not}) nor (\ref{have not}) are ambiguous. In (\ref{could not}), we express the fact that Billy was unable to go before our arrival. In (\ref{have not}), we express the possibility Billy was able to \emph{not} go, but in a world where Billy did go, (\ref{have not}) may still be true. 703 | 704 | %Real world knowledge JR 705 | 706 | Thus even in a single language our generalization holds. 707 | Syntactic rigidity allows for ambiguity, while free flexibility creates situations where ambiguity is ruled out due to the assumption that speakers have that surface scope is universally preferred. 708 | 709 | This is not just true from language to language or construction to construction, but in English, even when specifically addressing negation, \emph{any} higly local syntactic rigidity causes ambiguity and \emph{any} highly local syntactic flexibility disambiguates. 710 | 711 | And as expected, languages that can syntactically bear negation before all modals/verbs, such as Chinese do not create the ambiguity in the rigid English example \parencite{ernst98}. 712 | 713 | \begin{exe} 714 | \ex{\gll Shujuan keyi bu gen Guorong {tiao wu}.\\ 715 | S. may not with G. dance\\ 716 | \trans{``Shujuan may not dance with Guorong.''} \hfill (may $>$ not; *not $>$ may) } 717 | \ex{\gll Shujuan bu keyi gen Guorong {tiao wu}.\\ 718 | S. not may with Guorong dance\\ 719 | \trans{``Shujuan may not dance with Guorong.''} \hfill (not $>$ may; *may $>$ not)} 720 | \end{exe} 721 | 722 | The Persian situation is particularly interesting. In most situations, while noun scrambling is mostly free, scrambling of the verb and its negation is more marked. This manifests in that inverse scope is very possible in positions involving a negation interfacing with another quantifier. 723 | 724 | \begin{exe} 725 | \ex {\gll Yek d\=aneshju \=an ket\=ab-r\=a na-x\=and. \\ 726 | one student that book-ACC not-read \\ 727 | \trans{``A student didn't read that book.\label{par}''}} 728 | \end{exe} 729 | 730 | As we would predict, (\ref{par}) is ambiguous. It can mean either a certain student didn't read the book ($\exists > \neg$) or that \emph{not one} student read it ($\neg > \exists$). This ambiguity arises because the movement of the verb is more marked. 731 | 732 | In other situations, particularly in movement verbs, the Persian main verb becomes more flexible. SVO order, where the negation is still a pre-verbal clitic, is common with some movement verbs, and as expected, the ambiguity evaporates in (\ref{pm1}) and (\ref{pm2}). 733 | 734 | \begin{exe} 735 | \ex{\gll Billy na-raft hame shahr-i.\\ 736 | B. not-went all city-IND\\ 737 | \trans{``Billy didn't go to every city.'' \hfill ($\neg > \forall$; *$\forall > \neg$)\label{pm1}} 738 | } 739 | \ex{\gll Billy be hame shahr-i na-raft.\\ 740 | B. to all city-IND not-went.\\ 741 | \trans{``Billy didn't go to any city.'' \hfill ($\forall > \neg$; *$\neg > \forall$)\label{pm2}} 742 | } 743 | \end{exe} 744 | 745 | 746 | \subsubsection{Construction-specific Rigidity} 747 | 748 | Since my statement here is that scope ambiguity is merely the result of linear rigidity in syntax, not of some language-wide parameter, we should see the unambiguous surface scope of scrambling languages disappear in particular constructions where normally scramblible nominals are tied in position. 749 | 750 | Chinese, usually a very stablely scrambling or discourse configurational language generally allows the low cost movement of nominals as illustrated in (\ref{chin}) (from \textcite{aoun93}). These sentences, as we should expect are unambiguous and force surface scope. In (\ref{chin1}), everyone arrests different women, while in (\ref{chin2}), only one woman, who apparently is a prolific criminal, is arrested. 751 | 752 | \begin{exe} 753 | \ex \begin{xlist}\label{chin} 754 | \ex[]{\gll Meigeren dou zhuazou yige {n\"uren}.\\ 755 | everyone all arrest a woman\\ 756 | \trans{``Everyone arrested a woman.''\label{chin1}} 757 | } 758 | \ex[]{\gll (You) yige {n\"uren} meigeren dou zhuazou.\\ 759 | (have) a woman everyone all arrest.\\ 760 | \trans{``A woman was arrested by everyone.''\label{chin2}} 761 | }\end{xlist} 762 | \end{exe} 763 | 764 | However Chinese \emph{bei} pseudo-passives require a particular word order. The semantic object is promoted as the initial nominal, while the agent follows the preverbal co-verb ``bei'' as shown in (\ref{chin3}). As (\ref{chin4}) shows, however, the quasi-prepositional \emph{bei} $+$ \emph{agent} constituent may not be fronted or topicalized. 765 | 766 | \begin{exe} 767 | \ex{ \begin{xlist} 768 | \ex[]{\gll Meigeren dou bei yige {n\"uren} zhuazou.\\ 769 | everyone all PASS a woman arrest\\ 770 | \trans{``Everyone was arrested by a woman.''\label{chin3}} 771 | } 772 | \ex[*]{Bei yige {n\"uren} meigeren dou zhuazou.\\ 773 | PASS a woman everyone all arrest\\ 774 | \label{chin4} 775 | }\end{xlist}} 776 | \end{exe} 777 | 778 | The scopal possibilities follow the predictions perfectly. Since flexible word order is unavailable, (\ref{chin3}) is ambiguous: there can either be one woman arresting everyone, or each person can be arrested by a different woman. 779 | 780 | Interestingly enough, the scope possibilities in Chinese in normal clauses and the \emph{bei} pseudo-passive are precisely the opposite of English, again this falls out from the fact that nominal movement is generally free in Chinese (meaning unambiguous sentences normally) and the additional fact that \emph{bei} passives are not precisely equivalent to their active counterparts, but add additional meaning.\footnote{\emph{Bei} passives imply some kind of misfortune or negativity. Thus (\ref{chin3}) could be translated as ``Everyone befell arresting by a woman'' or something of the sort.} 781 | 782 | On a philological note, it might be that languages with free word-order like Chinese probably use transformations less than rigid word-order languages like English specifically because they are unnecessary for scope. Those transformations they do use, like \emph{bei} passives, may tend to have extra semantic value lest they be ``worthless.'' 783 | 784 | 785 | \section{Theoretical Issues Solved and Opened} 786 | 787 | \subsection{The Gambit of Linear Order} 788 | 789 | It should be noted that the data of scope present an existential problem for the general interpretation of syntax from a ``logical form'' perspective. On one hand, the assumption has been that scope interpretations are read from quantificational elements which interface with the hierarchical structure of language. This structure (from the Chomskyan perspective) is construed as irrelevant to the linear order of a sentence, which is a later realization of the expression in phonological form. 790 | 791 | But the overwhelming reality of scope as a feature of natural language is that it is manifestly and abundantly tied to linear order, nearly all of the data presented here, along with that in the literature testify to this. 792 | 793 | I think a proper understand of scope would be that \emph{all possible scope readings of all sentences are theoretically possible at all times}. In normal discoursive situations, however, most possible readings as pruned out as implausible, based on pragmatic circumstances or world-knowledge. This also would attest well the conundrum of every syntax class, where graduate students sit around long enough looking at sentences without context and start seeing \emph{all} of the scopal readings after long enough. My analysis here has endeavored to show why some readings are \emph{ruled out} in certain situations, although this is no be-all-end-all solution to scope, precisely because it is a pragmatic, and perhaps extralinguistic portion of language. 794 | 795 | Such a framework would be able to maintain the statement that human language, at its syntactic core, should be independent of linear order, as the linear order effects are part of the pragmatic traits of language use and discourse. 796 | 797 | \subsection{Scope Interpretations are Not Licensed, but \emph{Pruned}} 798 | 799 | Again, I have not crafted a universal account of scope ambiguities, and have deliberately avoid some contradictory examples that I think explicable on other grounds. Take the sentence pair below. 800 | 801 | \begin{exe} 802 | \ex Every boy ate an apple.\label{evboy} 803 | \ex An apple was eaten by every boy.\label{anap} 804 | \end{exe} 805 | 806 | (\ref{evboy}) follows the generalizations we've sketched here in, that it is ambiguous ($\forall>\exists$, $\exists>\forall$). (\ref{anap}), as a passive, is unambiguous, but not in the way we've predicted here, but \emph{only} inverse scope is allowed ($\forall>\exists$, *$\exists>\forall$), or at least, inverse scope is highly preferred. 807 | 808 | 809 | What rules out the surface scope interpretation of (\ref{anap}) is not the pragmatics of passivization \emph{per se}, but the interface of general world knowledge with the inherent telicity of the verb \emph{eat} with a count noun object. The predicate ``ate an apple'' implies that the subject totally consumed an apple, but if the universal quantifier is thought to scope over the existential ``an apple,'' this would have to mean that every boy totally ate the same apple as every other boy, which is logically impossible. 810 | 811 | This makes the otherwise disfavored $\forall>\exists$ interpretation the only logically consistent option. If we rejigger the sentence to remove the telicity, as in (\ref{jig}), we see that the expected scope possibilities return, even when the sentence is still somewhat strange by that interpretation. 812 | 813 | \begin{exe} 814 | \ex Some of an apple was eaten by every boy. \hfill ($\exists>\forall$, $\forall>\exists$)\label{jig} 815 | \end{exe} 816 | 817 | Note \emph{also} that if we imagine (\ref{anap}) in a discourse environment, we're most likely to think of constrastive focus or something else: ``An apple was eaten by every boy, a banana by every woman, a pineapple by every man\ldots'' 818 | 819 | I do \emph{not} consider this a contradiction, but evidence in favor of the wider point. 820 | Scope ambiguities are trimmed away by pragmatic factors. In (\ref{anap}), it is world knowledge, in most of the other examples here, it's economy of derivation. 821 | 822 | \section{Closing} 823 | 824 | %Everyone believes that some person loves a dog. 825 | 826 | In closing, much of the confusion about scope can be alleviated by understanding that scope availabilities are determined by pragmatic factors and implicatures that can be modelled Game Theoretically. We've seen here that the facts about the scope availabilities of most languages fall out quite effortlessly from assumptions about the cost of transformations, the costlessness of scrambling and the wider syntactic capacities of a language. 827 | 828 | I feel that much more work can be note to resolve questions in scope using pragmatic facts, particularly in the areas of telicity and world knowledge. Regardless, there seems to be decent circumstantial evidence to lend credence to the idea that scope is not a component of narrow syntax, but a set of extra-UG implicatures we make about language use. 829 | 830 | Additionally, other factors of grammar, such as binding in the classical sense are in need of new life, once insurmountable problems were brought to traditional syntactic analyses of the data. It may be that these other factors, binding, negative polarity items and cross-over effects may actually be derivable on pragmatic grounds, and thus would eliminate such of the theoretical mess and greatly economize and minimize the core language faculty. 831 | 832 | 833 | 834 | \begin{figure} 835 | \begin{tabular}{rl} 836 | Abrv.& Strategy name\\ 837 | A & \textbf{A}ctive Voice (Speaker)\\ 838 | P & \textbf{P}assive Voice (Speaker)\\ 839 | S & Interpret \textbf{S}urface scope (Hearer)\\ 840 | I & Interpret \textbf{I}nverse scope (Hearer)\\ 841 | \end{tabular} 842 | \end{figure} 843 | 844 | 845 | 846 | \printbibliography 847 | 848 | \end{document} 849 | -------------------------------------------------------------------------------- /pres.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/pres.pdf -------------------------------------------------------------------------------- /pres.tex: -------------------------------------------------------------------------------- 1 | \documentclass[aspectratio=1610]{beamer} 2 | \usepackage{forest} 3 | \usepackage{cgloss4e} 4 | \usepackage{tikz} 5 | \usepackage{gb4e} 6 | \usetheme{Boadilla} 7 | \usetikzlibrary{calc} 8 | \usetikzlibrary{matrix} 9 | \usetikzlibrary{positioning} 10 | 11 | \title{Scope without Syntax} 12 | \subtitle{Towards a Game Theoretic Approach} 13 | \author{Luke Smith} 14 | \institute{Committee: Robert, MPP, TgB} 15 | \usetikzlibrary{shapes.geometric, arrows} 16 | 17 | \tikzset{Above/.style={midway,above,font=\scriptsize,text width=1.5cm,align=center,},Below/.style={midway,below,font=\scriptsize,text width=1.5cm,align=center}} 18 | \tikzstyle{box} = [rectangle, centered, draw=black,minimum width=3cm, minimum height=1cm] 19 | \tikzstyle{arrow} = [thick,->,>=stealth] 20 | 21 | \tikzset{centered/.style=} 22 | 23 | 24 | \begin{document} 25 | 26 | \resetcounteronoverlays{exx} 27 | 28 | \begin{frame} 29 | \titlepage 30 | \end{frame} 31 | 32 | \section{Background} 33 | 34 | \begin{frame} 35 | \frametitle{Quantifiers}\pause 36 | \begin{itemize} 37 | \item Languages have what are called \emph{quantifiers}, which are words which delineate particular quantities of nouns that they modify.\pause 38 | \begin{itemize} 39 | \item \textbf{Universal quantifiers} -- all, each, every ($\forall$)\pause 40 | \item \textbf{Existential quantifiers} -- a, one, some ($\exists$)\pause 41 | \item \textbf{Negation} -- not, no ($\neg$)\pause 42 | \item Many others -- numerals, much, many, few, etc.\pause 43 | \end{itemize} 44 | 45 | \item For the purposes of sentence interpretation, quantifiers are quite a puzzle. Especially when there are multiple quantifiers in a sentence, a sentence may become ambiguous. 46 | \end{itemize} 47 | 48 | \end{frame} 49 | 50 | \begin{frame} 51 | \frametitle{Scope Ambiguity}\pause 52 | \begin{exe} 53 | \ex Everyone loves someone. 54 | \end{exe}\pause 55 | \begin{itemize} 56 | \item This sentence has two quantifiers, a universal ($\forall$) `every' and an existential ($\exists$) `some.'\pause 57 | \item This sentence has two different interpretations:\pause 58 | \begin{itemize} 59 | \item For each person, there exists some other person they love.\pause 60 | \item There exists one particular person who everyone loves.\pause 61 | \end{itemize} 62 | \item In the first possible reading, we say that the $\forall$ takes `wide scope' over the $\exists$, which is said to have `narrow scope.'\pause 63 | 64 | \item In the second, we say that the $\exists$ takes wide scope over the $\forall$. 65 | \end{itemize} 66 | \end{frame} 67 | 68 | \section{Scope in the Field} 69 | 70 | \begin{frame} 71 | \frametitle{Traditional View}\pause 72 | \begin{itemize} 73 | \item Scope was traditionally dealt with in terms of `movement' and `logical form.' An ambiguous sentence had to go through some kind of post-syntactic change to yield an unambiguous representation in the mind.\pause 74 | \item Different languages were discovered to have different availabilities of scope ambiguity. This was dealt with with formal and syntactic changes.\pause 75 | \item Not so important to go into because basically nothing worked across wide data sets.\pause 76 | \item Scope ambiguity is difficult to account for because it is:\pause 77 | \begin{itemize} 78 | \item Highly context sensitive (Chomsky's aphasia)\pause 79 | \item Sensitive to linear order 80 | \end{itemize} 81 | \end{itemize} 82 | \end{frame} 83 | 84 | \begin{frame} 85 | \frametitle{Game Theoretic Scope}\pause 86 | \begin{itemize} 87 | \item \textbf{My statement:} Scope ambiguity is totally paralinguistic. Scope ambiguities fall out from listeners' evaluation of the intentions of the speaker.\pause 88 | \item This can partially be modeled in Game Theory, seeing that speakers are mutually evaluating the others' behavior and choosing how to word or interpret sentences based on that.\pause 89 | \item This can allow us to formally analyze an apparent ``functional'' alternation. 90 | \end{itemize} 91 | \end{frame} 92 | 93 | \begin{frame} 94 | \frametitle{The Game} 95 | 96 | \begin{figure} 97 | \begin{center} 98 | \begin{tikzpicture}[node distance=2cm] 99 | 100 | \node (nature) [box, align=center] {{\large \textbf{ Player 0: ``Nature''}}\\Determines desired quantifier scope interpretation $s$}; 101 | \node (speaker) [box, align=center, below of=nature] {{\large \textbf{Player 1: ``Speaker''}}\\Determines a best wording $w$ to communicate $s$ }; 102 | \node (hearer) [box, align=center, below of=speaker] {{\large \textbf{Player 2: ``Hearer''}}\\Must guess $s$ based $w$}; 103 | 104 | \draw [arrow] (nature) -- (speaker) ; 105 | \draw [arrow] (speaker) -- (hearer) ; 106 | \end{tikzpicture} 107 | \end{center} 108 | \end{figure} 109 | \end{frame} 110 | 111 | 112 | 113 | 114 | \begin{frame} 115 | \frametitle{Precedents in Linguistics}\pause 116 | \begin{itemize} 117 | \item Game Theory has been similarly employed in linguistics, particularly semantics to deal with implicatures.\pause 118 | \begin{exe} 119 | \ex Billy ate most of the chocolates. 120 | \end{exe}\pause 121 | \item Sentences like this in actual language are inferred to mean that Billy ate most \emph{but not all chocolates}, although the sentence is logically still true if he did.\pause 122 | \item However speakers \emph{assume} Billy didn't eat \emph{all} the chocolates because if that were true, a speaker probably would've said so. 123 | \end{itemize} 124 | \end{frame} 125 | 126 | 127 | \section{Potential Solution} 128 | 129 | \begin{frame} 130 | \frametitle{Assumptions and Constraints} 131 | \begin{itemize}\pause 132 | \item It is generally preferable if quantifiers occur in the order they are supposed to be interpreted in (surface scope).\pause 133 | \item Moving around nouns via `transformations' (passivization, clefting, etc.) is costly/marked/undesirable.\pause 134 | \item Scrambling (to be discussed later), as opposed to transformations are not similarly costly. 135 | \end{itemize} 136 | \end{frame} 137 | 138 | 139 | \begin{frame} 140 | \frametitle{English Data}\pause 141 | \begin{itemize} 142 | \item Typical English sentences show scope ambiguity if there is more than one quantifier:\pause 143 | \begin{exe} 144 | \ex Two men dug each hole. 145 | \end{exe}\pause 146 | \item There can be two particular men who dig all the holes ($\exists>\forall$) or, each hole can be dug by a different pair of men ($\forall>\exists$) .\pause 147 | \item Ambiguity will usually disappear or become highly dispreferred if the sentence undergoes a `transformation:'\pause 148 | \begin{exe} 149 | \ex Each hole was dug by two men. 150 | \end{exe}\pause 151 | \item Here, the strongly preferred reading is the one where there is a pair of men for each hole ($\forall>\exists$), while the case where there is two specific men for each hole is harder to get out of the blue. 152 | \end{itemize} 153 | \end{frame} 154 | 155 | \begin{frame} 156 | \frametitle{English Data}\pause 157 | \begin{exe} 158 | \ex Everyone loves someone.\pause 159 | \ex Everyone loves someone, and that person is Billy.\pause 160 | \ex Everyone loves someone. Don't pretend like you don't have someone special.\pause 161 | \ex Someone is loved by everyone.\pause 162 | \ex Someone is loved by everyone, and that person is Billy.\pause 163 | \ex[??]{ Someone is loved by everyone. Don't pretend like you don't have someone special.} 164 | \end{exe} 165 | \end{frame} 166 | 167 | \begin{frame} 168 | \frametitle{The Payoffs}\pause 169 | 170 | \begin{itemize} 171 | \item Both Players receive a payoff when the sentence is correctly communicated, represented by $x$.\pause 172 | \item If the more marked inverse scope is employed, both players suffer a slightly diminished payoff. We we refer to this amount as $i$.\pause 173 | \item If the Speaker employs passive voice, he suffers a slight loss $p$.\pause 174 | \item $|p+i|<|x|$ That is, even if we have to passivize and get inverse scope interpretation, it's always most preferable to get the intended interpretation. 175 | \end{itemize} 176 | 177 | \end{frame} 178 | 179 | \begin{frame} 180 | \frametitle{The Decision Tree} 181 | \begin{figure} 182 | \begin{forest} 183 | for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 184 | (.child anchor)\forestoption{edge label}; 185 | }, 186 | l sep=2cm, 187 | } 188 | [Nature,rectangle, s sep=25pt, 189 | [Speaker,edge label={node[Below]{$\exists>\forall$}} 190 | [Hearer,edge label={node[Below]{Passive}} 191 | [{$-p-i,-i$},edge label={node[Below]{Inverse}}] 192 | [{$x-p,x$},edge label={node[Below]{Surface}}] 193 | ] 194 | [Hearer,edge label={node[Above]{Active}} 195 | [{$x-i,x-i$},edge label={node[Below]{Inverse}}] 196 | [{$0,0$},edge label={node[Below]{Surface}}] 197 | ] 198 | ] 199 | [Speaker,edge label={node[Above]{$\forall>\exists$}} 200 | [Hearer,edge label={node[Below]{Passive}} 201 | [{$x-p-i,x-i$},edge label={node[Below]{Inverse}}] 202 | [{$-p,0$},edge label={node[Below]{Surface}}] 203 | ] 204 | [Hearer,edge label={node[Above]{Active}} 205 | [{$-i,-i$},edge label={node[Below]{Inverse}}] 206 | [{$x,x$},edge label={node[Below]{Surface}}] 207 | ] 208 | ] 209 | ] 210 | \end{forest} 211 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 212 | \end{figure} 213 | \end{frame} 214 | 215 | \begin{frame}[fragile] 216 | \frametitle{Matrix for when Nature chooses $\forall > \exists$} 217 | \begin{center} 218 | \begin{figure} 219 | \begin{tikzpicture} 220 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 221 | $x$&$-y$\\ 222 | $x$&$0$\\ 223 | $-i$&$x-p-i$\\ 224 | $-i$&$x-i$\\ 225 | }; 226 | \draw (m.north east) rectangle (m.south west); 227 | \draw (m.north) -- (m.south); 228 | \draw (m.east) -- (m.west); 229 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 230 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 231 | \node[above=5pt of a,anchor=base] {Active}; 232 | \node[above=5pt of b,anchor=base] {Passive}; 233 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 234 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 235 | \node[left=2pt of c,text width=1cm] {Surface}; 236 | \node[left=2pt of d,text width=1cm] {Inverse}; 237 | \node[above=18pt of m.north] (firm b) {Speaker}; 238 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 239 | \end{tikzpicture} 240 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 241 | \end{figure} 242 | \end{center} 243 | \end{frame} 244 | 245 | \begin{frame}[fragile] 246 | \frametitle{Matrix for when Nature chooses $\exists > \forall$} 247 | \begin{center} 248 | \begin{figure} 249 | \begin{tikzpicture} 250 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 251 | $0$&$x-p$\\ 252 | $0$&$x$\\ 253 | $x-i$&$-p-i$\\ 254 | $x-i$&$-i$\\ 255 | }; 256 | \draw (m.north east) rectangle (m.south west); 257 | \draw (m.north) -- (m.south); 258 | \draw (m.east) -- (m.west); 259 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 260 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 261 | \node[above=5pt of a,anchor=base] {Active}; 262 | \node[above=5pt of b,anchor=base] {Passive}; 263 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 264 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 265 | \node[left=2pt of c,text width=1cm] {Surface}; 266 | \node[left=2pt of d,text width=1cm] {Inverse}; 267 | \node[above=18pt of m.north] (firm b) {Speaker}; 268 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 269 | %\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$ in a scrambling language}; 270 | \end{tikzpicture} 271 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 272 | \end{figure} 273 | \end{center} 274 | \end{frame} 275 | \begin{frame} 276 | \frametitle{Scope in Scrambling Languages}\pause 277 | \begin{itemize} 278 | \item English has relatively rigid word order (subject-verb-object), but many languages have what is called `scrambling' which is free linear movement of nouns without the cost of transformations.\pause 279 | \item Scope is systematically different in languages like these.\pause 280 | \end{itemize} 281 | \begin{exe} 282 | \ex {\gll Har d\=aneshjui ye kit\=abi-ro mixune.\\ 283 | all student a book-OBJ reads\\ 284 | \trans{``Every student is reading a book.''}}\pause 285 | \ex {\gll Ye ket\=abi-ro har d\=aneshjui mixune.\\ 286 | a book-OBJ all student reads\\ 287 | \trans{``Every student is reading a book.''}} 288 | \end{exe}\pause 289 | \begin{itemize} 290 | \item However, both of these sentences \emph{must have} \textbf{surface scope}. They cannot be ambiguous. 291 | \end{itemize} 292 | \end{frame} 293 | 294 | \begin{frame} 295 | \frametitle{A Game Theoretic Account}\pause 296 | \begin{itemize} 297 | \item Given our previous suggested constraints, we can predict these scope availabilities.\pause 298 | \item Remember, \textbf{surface scope} is preferred and \textbf{transformations} are costly. 299 | \end{itemize} 300 | \end{frame} 301 | 302 | \begin{frame} 303 | \begin{figure} 304 | 305 | \footnotesize 306 | \begin{forest} 307 | for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 308 | (.child anchor)\forestoption{edge label}; 309 | }, 310 | l sep=2cm, 311 | } 312 | [Nature,rectangle, s sep=25pt, 313 | [Speaker,edge label={node[Below]{$\exists>\forall$}} 314 | [Hearer,edge label={node[Below]{Passive}} 315 | [{$-y-w,-w$},edge label={node[Below]{Inverse}}] 316 | [{$x-y,x$},edge label={node[Below]{Surface}}] 317 | ] 318 | [Hearer,edge label={node[Above]{Active}} 319 | [{$x-w,x-w$},edge label={node[Below]{Inverse}}] 320 | [{$0,0$},edge label={node[Below]{Surface}}] 321 | ] 322 | [Hearer, edge label={node[Above]{Scramble}} 323 | [{$-w,-w$}, edge label={node[Below]{Inverse}}] 324 | [{$x,x$}, edge label={node[Below]{Surface}}] 325 | ] 326 | ] 327 | [Speaker,edge label={node[Above]{$\forall>\exists$}} 328 | [Hearer,edge label={node[Below]{Passive}} 329 | [{$x-y-w,x-w$},edge label={node[Below]{Inverse}}] 330 | [{$-y,0$},edge label={node[Below]{Surface}}] 331 | ] 332 | [Hearer,edge label={node[Above]{Active}} 333 | [{$-w,-w$},edge label={node[Below]{Inverse}}] 334 | [{$x,x$},edge label={node[Below]{Surface}}] 335 | ] 336 | [Hearer, edge label={node[Above]{Scramble}} 337 | [{$x-w$}, edge label={node[Below]{Inverse}}] 338 | [{$0,0$}, edge label={node[Below]{Surface}}] 339 | ] 340 | ] 341 | ] 342 | \end{forest} 343 | \end{figure} 344 | 345 | \end{frame} 346 | 347 | \begin{frame} 348 | \frametitle{In an English-like language\ldots}\pause 349 | \begin{itemize} 350 | \item As assumed speakers \emph{want} to interpret quantifiers in linear order.\pause 351 | \item When a speaker produces a costly transformation (like a passive) the listener assumes that the new surface word order is the intended scope order.\pause 352 | \item If a speaker produces an untransformed sentence, the listener has two possible hypotheses: (1) the speaker intended surface scope, or (2) that the speaker intended inverse scope, but didn't want to undergo a costly transformation.\pause 353 | \item These two possibilities produce scope ambiguity. 354 | \end{itemize} 355 | \end{frame} 356 | 357 | 358 | \begin{frame} 359 | \frametitle{In Scrambling Languages}\pause 360 | \begin{itemize} 361 | \item In scrambling languages, since speakers have greater flexibility in ordering, listeners make different assumptions about intended scope.\pause 362 | \item If the speaker wants the object to scope over the subject, he can easily scramble it leftward.\pause 363 | \item Since he can do this, the unscrambled sentence has an unambiguous surface scope interpretation.\pause 364 | \item \textbf{Sidenote:} Potentially related, languages with scrambling/flexible word order, usually rely on things like passivization less often. 365 | \end{itemize} 366 | \end{frame} 367 | 368 | 369 | \begin{frame} 370 | \frametitle{Just a random difference?}\pause 371 | \begin{itemize} 372 | \item In addition to this correlation between rigid word-order and scrambling languages, we see that this theory still hold in rigid constructions in scrambling languages.\pause 373 | \item In Persian, for example, although nouns are flexible, negation must always be on the same part of a verb.\pause 374 | \item We should expect negative quantifiers to work similar to English sentences in that they produce ambiguity. This is the case:\pause 375 | \begin{exe} 376 | \ex {\gll Billy ye ket\=abi-ro na-xund.\\ 377 | Billy a book-OBJ not-read\\ 378 | \trans{``Billy didn't read a (particular) book.'' ($\exists>\neg$)or ``Billy didn't read any book.'' ($\neg>\exists$)}} 379 | \end{exe}\pause 380 | \item This holds in similar languages with scrambling and stable negation location (e.g. Korean). 381 | 382 | \end{itemize} 383 | \end{frame} 384 | 385 | \begin{frame} 386 | \frametitle{Rigidity = Ambiguity; Flexiblity = Unambiguousness} 387 | 388 | \begin{itemize} 389 | \item The general theorem that arises from this analysis is that \emph{wherever} we have syntactic flexibility, we have ambiguity (and \textit{vice versa}.) 390 | \item This difference, in agreement with our theory, is true \emph{across constructions}, not necessarily \emph{across languages}. 391 | \item ``Scrambling'' languages are unambiguous in normal sentences, but are in more rigid constructions, ambiguity arises. 392 | \begin{itemize} 393 | \item This is because the ambiguity is not a language-specific parameter, but a result of the strategies employable i any given context. 394 | \end{itemize} 395 | \end{itemize} 396 | 397 | \end{frame} 398 | 399 | \begin{frame} 400 | \frametitle{Local Rigidity}\pause 401 | In scrambling languages, generally we have syntactic flexibility accompanied by unambiguous surface scope.\pause 402 | 403 | \begin{exe} 404 | \ex \begin{xlist}\label{chin} 405 | \ex[]{\gll Meigeren dou zhuazou yige {n\"uren}.\\ 406 | everyone all arrest a woman\\ 407 | \trans{``Everyone arrested a woman.'' (${\forall}>{\exists} $)\label{chin1}}\pause 408 | } 409 | \ex[]{\gll (You) yige {n\"uren} meigeren dou zhuazou.\\ 410 | (have) a woman everyone all arrest.\\ 411 | \trans{``A woman was arrested by everyone.'' (${\exists}>{\forall}$)\label{chin2}} 412 | }\end{xlist} 413 | \end{exe}\pause 414 | 415 | But in syncactically inflexible constructions, ambiguity arises.\pause 416 | 417 | \begin{exe} 418 | \ex{ \begin{xlist} 419 | \ex[]{\gll Meigeren dou bei yige {n\"uren} zhuazou.\\ 420 | everyone all PASS a woman arrest\\ 421 | \trans{``Everyone was arrested by a woman.'' ($\forall > \exists$, ${\exists} > {\forall}$)\label{chin3}}\pause 422 | } 423 | \ex[*]{Bei yige {n\"uren} meigeren dou zhuazou.\\ 424 | PASS a woman everyone all arrest\\ 425 | \label{chin4} 426 | }\end{xlist}} 427 | \end{exe} 428 | \end{frame} 429 | 430 | 431 | \begin{frame} 432 | \frametitle{Goals and Intuitions}\pause 433 | \begin{itemize} 434 | \item Replace generative notions of syntactically-determined quantifier scope ambiguities with more plausible, externally-driven factors. 435 | \item Unify this account with other scope alternations (say, the unavailability of semantically implausible scope interpretations) into a general theory of scope where possible interpretations are \emph{pruned}, rather than derived by some syntactic engine. 436 | \end{itemize} 437 | \end{frame} 438 | 439 | \end{document} 440 | -------------------------------------------------------------------------------- /presented.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/LukeSmithxyz/scope-without-syntax/9f913d4acff2514a93884929d5536ef20bd3587c/presented.pdf -------------------------------------------------------------------------------- /rob: -------------------------------------------------------------------------------- 1 | Hi Luke, 2 | 3 | I've had a chance to write up some comments for your paper. As I said 4 | before, I'm sorry I couldn't be at your s-circle talk. I heard it was good 5 | and generated good discussion! 6 | 7 | I'm pasting the comments below. If you want to get together sometime to 8 | chat about them, i would be totally willing. I would also be happy to read 9 | a current try or parts of a draft of anything you're currently working on. 10 | 11 | Take care! 12 | 13 | Robert 14 | 15 | 16 | Overall comments 17 | ---------------- 18 | 19 | I think the paper is overall really nice. You have a good collection of 20 | data here, and the data are well-marshaled toward your analytical aims. 21 | Also, your explanations of the game-theoretic calculations to determine 22 | scope interpretations are really nice. I think, for me, there are a few 23 | high level things that you should probably think about. 24 | 25 | -- It would be really nice to have a deeper explanation for what makes a 26 | transformation costless or not. I don't think this needs to be completely 27 | solved, but some analytical intuitions about how to deal with this would 28 | really help deliver your argument with a punch. Of the top I my head 29 | 30 | -- Have you thought at all about other architectures? This is connected to 31 | a point I raise down below about pg3. For instance, you could redo this 32 | with bayesian signaling games where the hearer is trying to determine the 33 | probability of message m given signal s (a conditional probability), while 34 | the speaker is trying to choose a signal that maximizing the probability 35 | that the hearer will recover it. Utility of choices is then just waited 36 | against the probability that messages are recovered modified by costs. I 37 | bringing up this up because it seems to more amendable to a talking about 38 | tendencies as opposed to hard grammaticality, and you could even 39 | experimentally predict how often listeners should predict an interpretation 40 | given a form. We could talk more about it, but maybe you could raise this 41 | as a possibility for future work as a way to fight against my critique 42 | about pg3. 43 | 44 | -- There are related scope effects that I wonder if you can address. For 45 | instance, even in English which allows inverse scope, it is harder for 46 | universals to take inverse scope over indefinites than vice versa: Every 47 | man loves a women vs. A man loves every woman. Do you have an idea about 48 | how to extend your system to other things that affect scope? Would you just 49 | add more payoff penalties, etc.? 50 | 51 | -- Syntactic scope and interpretation are different. For instance, a 52 | logical form like "for all x [MAN(x) implies exists y[DOG(y) and 53 | LOVE(x,y)]] has the surface scope **structure** but is consistent (i.e., 54 | true) in a scenarios where every man happens to love the same dog (which 55 | might account for some of the effect in the previous point). I just think 56 | it would be nice for you to maybe address this point somehow---that is, the 57 | point that your (3b) doesn't like the indefinite taking scope over "every", 58 | but that it can't even have an in-situ wide scope interpretation. 59 | 60 | ######## 61 | 62 | I also have some smaller comments, mostly about issues of presentation. 63 | 64 | pg1 65 | 66 | I wouldn't use "battle of the sexes" here. I don't think that speakers and 67 | hearers are really in competition. It's that the interpretations are in 68 | competition and the speakers are trying to maximize utility (a component of 69 | which involves successful coordination). I might try to just rephrase this 70 | without the metaphor and make it clear what's competing and to what end. 71 | 72 | pg2 73 | 74 | I might rephrase this paragraph about payoffs to make it clearer that what 75 | you're doing is that you are encoding these assumption about scope into the 76 | model from which you will then make a series of nice predictions. I'm just 77 | worried uncharitable readers will look at sentences like: 78 | 79 | "If transformations, specifically passives, are costly or dis-preferred in 80 | some way, we can model them as saying that they reduce the payoff to the 81 | speaker to some degree (−y)" 82 | 83 | And saying, this doesn't model anything, but instead formalizing an 84 | assumption. Just make it clear that these are starting assumptions from 85 | which cool facts will be derived. 86 | 87 | pg3 88 | 89 | I am a bit skeptical of a hard grammatical constraint on inverse scope 90 | readings in passives. I think all things being equal they are 91 | dis-preferred, but you can make them good. Consider the fact that 92 | appositives on indefinites privileged the singleton reading. If that is 93 | true and if your constraint is hard, then the following should seem 94 | ungrammatical, but it seems fine to me. 95 | 96 | Every watermelon was eaten by a man, who sneaked into the picnic when we 97 | weren't looking. 98 | 99 | I would really like a theory that says inverse scope is not barred in these 100 | scenarios, but the pays are such that they are strongly dis-preferred all 101 | things being equal. What do you think? 102 | 103 | 104 | -- 105 | Assistant Professor of Linguistics 106 | University of Arizona 107 | -------------------------------------------------------------------------------- /showcase.rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Quantifier Scope is Just All Fun and Games!" 3 | author: "Luke Smith" 4 | institute: "University of Arizona" 5 | header-includes: 6 | - \usecolortheme[dark]{solarized} 7 | - \usepackage{tikz} 8 | - \usepackage{gb4e} 9 | - \usetikzlibrary{calc} 10 | - \usetikzlibrary{matrix} 11 | - \usetikzlibrary{positioning} 12 | bibliography: /home/luke/Documents/LaTeX/uni.bib 13 | output: 14 | beamer_presentation: 15 | pandoc_args: ['--pdf-engine=xelatex'] 16 | classoption: "aspectratio=1610" 17 | --- 18 | 19 | # Quantifier Scope Basics 20 | 21 | Languages have quantifiers: 22 | 23 | >- **Universal quantifiers**, $(\forall)$: all, each, every 24 | >- **Existential quantifiers**, $(\exists)$: a, some, one 25 | >- And many others: numbers (3, 4, 5), most, few, etc. 26 | 27 | # The Problem with Scope 28 | 29 | Scope presents some unique problems: 30 | 31 | >- It is highly sensitive to linear order. (Surface scope preference.) 32 | >- Judgements vary a lot and are highly context-dependent. (Chosmky's aphasia) 33 | >- Scope is used in syntax, but less systematic than could be. 34 | 35 | # Scope without Syntax 36 | 37 | >- Solving for these traits and tendencies within syntax requires stipulating a lot in whatever grammatical theory you have. 38 | >- Instead: Quantifier scope is computed outside of the narrow language faculty. 39 | 40 | # Game Theory 41 | 42 | >- Tool for modeling strategic decision-making [@neumann44]. 43 | >- $n$ number of **Players**, which can be people or abstraction. 44 | >- Each Player has a certain number of **Strategies** that they can choose from. 45 | >- Depending on the strategies chosen, players get **Payoffs**. 46 | >- Players might have knowledge of other players' decisions or not, or their interests might be aligned or not, etc. etc... 47 | 48 | # Scope 49 | 50 | >- Language is game played between a Speaker and Hearer. 51 | >- Speakers have different constructions/sentences they can use as strategies. 52 | >- Some constructions are marked or dispreferred (passives, clefts, inverse scope). 53 | >- Hearer's strategies are the different ways to interpret a potentially ambiguous sentence. 54 | >- Speakers and Hearers both want to reach a mutual understanding (non-zero sum). 55 | 56 | # The Game Tree for English 57 | 58 | \begin{figure} 59 | \begin{center} 60 | \tikzstyle{level 1}=[level distance=1.5cm, sibling distance=6.5cm] 61 | \tikzstyle{level 2}=[level distance=1.5cm, sibling distance=3cm] 62 | \tikzstyle{level 3}=[level distance=1.5cm, sibling distance=1.75cm] 63 | \tikzstyle{level 4}=[level distance=1.5cm, sibling distance=2cm] 64 | \begin{tikzpicture} 65 | \node {Nature} 66 | child{ 67 | node{Speaker} 68 | child{ 69 | node(d){Hearer} 70 | child{ 71 | node{$\displaystyle\binom{c}{c}$} 72 | edge from parent 73 | node[left]{$S$} 74 | } 75 | child{ 76 | node{$\displaystyle\binom{-i}{-i}$} 77 | edge from parent 78 | node[right]{$I$} 79 | } 80 | edge from parent 81 | node[left]{$A$} 82 | } 83 | child{ 84 | node(a){Hearer} 85 | child{ 86 | node{$\displaystyle\binom{-p}{0}$} 87 | edge from parent 88 | node[left]{$S$} 89 | } 90 | child{ 91 | node{$\displaystyle\binom{c-p-i}{c-i}$} 92 | edge from parent 93 | node[right]{$I$} 94 | } 95 | edge from parent 96 | node[right]{$P$} 97 | } 98 | edge from parent 99 | node[left]{${Sub}>{Obj}$} 100 | } 101 | child{ 102 | node{Speaker} 103 | child{ 104 | node(b){Hearer} 105 | child{ 106 | node{$\displaystyle\binom{0}{0}$} 107 | edge from parent 108 | node[left]{$S$} 109 | } 110 | child{ 111 | node{$\displaystyle\binom{c-i}{c-i}$} 112 | edge from parent 113 | node[right]{$I$} 114 | } 115 | edge from parent 116 | node[left]{$A$} 117 | } 118 | child{ 119 | node(c){Hearer} 120 | child{ 121 | node{$\displaystyle\binom{c-p}{c}$} 122 | edge from parent 123 | node[left]{$S$} 124 | } 125 | child{ 126 | node{$\displaystyle\binom{-p-i}{-i}$} 127 | edge from parent 128 | node[right]{$I$} 129 | } 130 | edge from parent 131 | node[right]{$P$} 132 | } 133 | edge from parent 134 | node[right]{${Obj}>{Sub}$} 135 | }; 136 | \draw [dashed](d)to[in=180](b); 137 | \draw [dashed](a)to[in=180](c); 138 | \end{tikzpicture} 139 | \end{center} 140 | \end{figure} 141 | 142 | * $c$ for sucessful communication. 143 | * $p$ as a penalty for using the passive. 144 | * $i$ as a penalty for inverse scope. 145 | 146 | # What about a scrambling language? 147 | 148 | >- There is a "costless" alternative to the passive which does the same thing. 149 | 150 | \begin{exe} 151 | \ex asdfsad 152 | \ex sadasahsdkjf 153 | \end{exe} 154 | 155 | # Extensions 156 | 157 | >- The anaylsis isn't over. 158 | >- Myself, GMP, RWS and Robert Henderson are conspiring to extend the project. 159 | >- Empirical 160 | -------------------------------------------------------------------------------- /synsalon.tex: -------------------------------------------------------------------------------- 1 | \documentclass{beamer} 2 | \usepackage{forest} 3 | \usepackage{cgloss4e} 4 | \usepackage{tikz} 5 | \usepackage{gb4e} 6 | \usetheme{Boadilla} 7 | \usetikzlibrary{calc} 8 | \usetikzlibrary{matrix} 9 | \usetikzlibrary{positioning} 10 | 11 | \title{Scope without Syntax} 12 | \subtitle{Towards a Game Theoretic Approach} 13 | \author{Luke Smith} 14 | \date{September 27, 2017} 15 | \institute{Committee: Robert, MPP, TgB} 16 | \usetikzlibrary{shapes.geometric, arrows} 17 | 18 | \tikzset{Above/.style={midway,above,font=\scriptsize,text width=1.5cm,align=center,},Below/.style={midway,below,font=\scriptsize,text width=1.5cm,align=center}} 19 | \tikzstyle{box} = [rectangle, centered, draw=black,minimum width=3cm, minimum height=1cm] 20 | \tikzstyle{arrow} = [thick,->,>=stealth] 21 | 22 | \tikzset{centered/.style=} 23 | 24 | 25 | \begin{document} 26 | 27 | \resetcounteronoverlays{exx} 28 | 29 | \begin{frame} 30 | \titlepage 31 | \end{frame} 32 | 33 | \section{Background} 34 | 35 | \begin{frame} 36 | \frametitle{Quantifiers}\pause 37 | \begin{itemize} 38 | \item Languages have what are called \emph{quantifiers}, which are words which delineate particular quantities of nouns that they modify.\pause 39 | \begin{itemize} 40 | \item \textbf{Universal quantifiers} -- all, each, every ($\forall$)\pause 41 | \item \textbf{Existential quantifiers} -- a, one, some ($\exists$)\pause 42 | \item \textbf{Negation} -- not, no ($\neg$)\pause 43 | \item Many others -- numerals, much, many, few, etc.\pause 44 | \end{itemize} 45 | 46 | \item For the purposes of sentence interpretation, quantifiers are quite a puzzle. Especially when there are multiple quantifiers in a sentence, a sentence may become ambiguous. 47 | \end{itemize} 48 | 49 | \end{frame} 50 | 51 | \begin{frame} 52 | \frametitle{Scope Ambiguity}\pause 53 | \begin{exe} 54 | \ex Everyone loves someone. 55 | \end{exe}\pause 56 | \begin{itemize} 57 | \item This sentence has two quantifiers, a universal ($\forall$) `every' and an existential ($\exists$) `some.'\pause 58 | \item This sentence has two different interpretations:\pause 59 | \begin{itemize} 60 | \item For each person, there exists some other person they love.\pause 61 | \item There exists one particular person who everyone loves.\pause 62 | \end{itemize} 63 | \item In the first possible reading, we say that the $\forall$ takes `wide scope' over the $\exists$, which is said to have `narrow scope.'\pause 64 | 65 | \item In the second, we say that the $\exists$ takes wide scope over the $\forall$. 66 | \end{itemize} 67 | \end{frame} 68 | 69 | \section{Scope in the Field} 70 | 71 | \begin{frame} 72 | \frametitle{Traditional View}\pause 73 | \begin{itemize} 74 | \item Scope was traditionally dealt with in terms of `movement' and `logical form.' An ambiguous sentence had to go through some kind of post-syntactic change to yield an unambiguous representation in the mind.\pause 75 | \item Different languages were discovered to have different availabilities of scope ambiguity. This was dealt with with formal and syntactic parameters.\pause 76 | \item Over wide enough data sets, few generalizations were robust.\pause 77 | \item Scope ambiguity is difficult to account for because it is:\pause 78 | \begin{itemize} 79 | \item Highly context sensitive (Chomsky's aphasia)\pause 80 | \item Sensitive to linear order 81 | \end{itemize} 82 | \end{itemize} 83 | \end{frame} 84 | 85 | \begin{frame} 86 | \frametitle{Game Theoretic Scope}\pause 87 | \begin{itemize} 88 | \item \textbf{My statement:} Scope ambiguity is totally paralinguistic. Scope ambiguities fall out from listeners' evaluation of the intentions of the speaker.\pause 89 | \item We don't need ``syntax'', we don't need ``logical form'', we don't need any linguistic machinery whatsoever.\pause 90 | \item This can partially be modeled in Game Theory, seeing that speakers are mutually evaluating the others' behavior and choosing how to word or interpret sentences based on that.\pause 91 | \item This can allow us to formally analyze an apparent ``functional'' alternation. 92 | \end{itemize} 93 | \end{frame} 94 | 95 | \begin{frame} 96 | \frametitle{Game Theory Abridged} 97 | 98 | \begin{itemize} 99 | \item Theoretical framework for analyzing decision-making, conflict and cooperation.\pause 100 | \item The gist:\pause 101 | \begin{itemize} 102 | \item Have a set number of players.\pause 103 | \item Each player has a set of possible behaviors ``strategies''.\pause 104 | \item Players are awarded payoffs based on the strategies taken by each player. 105 | \end{itemize} 106 | \end{itemize} 107 | \end{frame} 108 | 109 | \begin{frame} 110 | \frametitle{Precedents in Linguistics}\pause 111 | \begin{itemize} 112 | \item Game Theory has been similarly employed in linguistics, particularly semantics to deal with implicatures.\pause 113 | \begin{exe} 114 | \ex Billy ate most of the chocolates. 115 | \end{exe}\pause 116 | \item Sentences like this in actual language are inferred to mean that Billy ate most \emph{but not all chocolates}, although the sentence is logically still true if he did.\pause 117 | \item However speakers \emph{assume} Billy didn't eat \emph{all} the chocolates because if that were true, a speaker probably would've said so.\pause 118 | \item Normal human:\pause 119 | \begin{itemize} 120 | \item ``If he wanted to say `Billy ate all the chocolates', he would've said just that!'' 121 | \end{itemize} 122 | \end{itemize} 123 | \end{frame} 124 | 125 | 126 | \begin{frame} 127 | \frametitle{Our Quantifier Scope Game} 128 | 129 | \begin{figure} 130 | \begin{center} 131 | \begin{tikzpicture}[node distance=2cm] 132 | 133 | \node (nature) [box, align=center] {{\large \textbf{ Player 0: ``Nature''}}\\Determines desired quantifier scope interpretation (${\forall}>{\exists}$ or ${\exists}>{\forall}$)}; 134 | \node (speaker) [box, align=center, below of=nature] {{\large \textbf{Player 1: ``Speaker''}}\\Determines a best wording to communicate Nature's chosen scope. }; 135 | \node (hearer) [box, align=center, below of=speaker] {{\large \textbf{Player 2: ``Hearer''}}\\Must guess Nature's choice based on the Speaker's.}; 136 | 137 | \draw [arrow] (nature) -- (speaker) ; 138 | \draw [arrow] (speaker) -- (hearer) ; 139 | \end{tikzpicture} 140 | \end{center} 141 | \end{figure} 142 | \end{frame} 143 | 144 | 145 | 146 | 147 | 148 | \section{Potential Solution} 149 | 150 | \begin{frame} 151 | \frametitle{Assumptions and Constraints} 152 | \begin{itemize}\pause 153 | \item It is generally preferable if quantifiers occur in the order they are supposed to be interpreted in (surface scope).\pause 154 | \item Moving around nouns via `transformations' (passivization, clefting, etc.) is costly/marked/undesirable.\pause 155 | \item Scrambling (to be discussed later), as opposed to transformations are not similarly costly. 156 | \end{itemize} 157 | \end{frame} 158 | 159 | 160 | \begin{frame} 161 | \frametitle{English Data}\pause 162 | \begin{itemize} 163 | \item Typical English sentences show scope ambiguity if there is more than one quantifier:\pause 164 | \begin{exe} 165 | \ex Two men dug each hole. 166 | \end{exe}\pause 167 | \item There can be two particular men who dig all the holes ($\exists>\forall$) or, each hole can be dug by a different pair of men ($\forall>\exists$) .\pause 168 | \item Ambiguity will usually disappear or become highly dispreferred if the sentence undergoes a `transformation:'\pause 169 | \begin{exe} 170 | \ex Each hole was dug by two men. 171 | \end{exe}\pause 172 | \item Here, the strongly preferred reading is the one where there is a pair of men for each hole ($\forall>\exists$), while the case where there is two specific men for each hole is harder to get out of the blue. 173 | \end{itemize} 174 | \end{frame} 175 | 176 | \begin{frame} 177 | \frametitle{English Data}\pause 178 | \begin{exe} 179 | \ex Everyone loves someone.\pause 180 | \ex Everyone loves someone, and that person is Billy.\pause 181 | \ex Everyone loves someone. Don't pretend like you don't have someone special.\pause 182 | \ex Someone is loved by everyone.\pause 183 | \ex Someone is loved by everyone, and that person is Billy.\pause 184 | \ex[??]{ Someone is loved by everyone. Don't pretend like you don't have someone special.} 185 | \end{exe} 186 | \end{frame} 187 | 188 | \begin{frame} 189 | \frametitle{Generalization in English}\pause 190 | 191 | \begin{itemize} 192 | \item Unmarked active sentences tend to be ambiguous.\pause 193 | \item Passive sentences tend to be unambiguous, preferring only surface scope. 194 | \end{itemize} 195 | 196 | \end{frame} 197 | 198 | \begin{frame} 199 | \frametitle{Now Onto the Game\ldots}\pause 200 | 201 | \begin{itemize} 202 | \item Both Players receive a payoff when the sentence is correctly communicated, represented by $x$.\pause 203 | \item If the more marked inverse scope is employed, both players suffer a slightly diminished payoff. We we refer to this amount as $i$.\pause 204 | \item If the Speaker employs passive voice, he suffers a slight loss $p$.\pause 205 | \item $|p+i|<|x|$ That is, even if we have to passivize and get inverse scope interpretation, it's always most preferable to get the intended interpretation.\pause 206 | \item This game is \textbf{non-zero sum Coordination Game}, meaning that both active players' interests are aligned.\pause 207 | \item The players \textbf{do not} have perfect information. While the Hearer knows what the Speaker's strategy is, he does not know what Nature has chosen. 208 | \end{itemize} 209 | 210 | \end{frame} 211 | 212 | \begin{frame} 213 | \frametitle{The Decision Tree} 214 | \begin{figure} 215 | \footnotesize 216 | \begin{forest} 217 | for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 218 | (.child anchor)\forestoption{edge label}; 219 | }, 220 | l sep=2cm, 221 | } 222 | [Nature,rectangle, s sep=25pt, 223 | [Speaker,edge label={node[Below]{$\exists>\forall$}} 224 | [Hearer,edge label={node[Below]{Passive}} 225 | [{$-p-i,-i$},edge label={node[Below]{Inverse}}] 226 | [{$x-p,x$},edge label={node[Below]{Surface}}] 227 | ] 228 | [Hearer,edge label={node[Above]{Active}} 229 | [{$x-i,x-i$},edge label={node[Below]{Inverse}}] 230 | [{$0,0$},edge label={node[Below]{Surface}}] 231 | ] 232 | ] 233 | [Speaker,edge label={node[Above]{$\forall>\exists$}} 234 | [Hearer,edge label={node[Below]{Passive}} 235 | [{$x-p-i,x-i$},edge label={node[Below]{Inverse}}] 236 | [{$-p,0$},edge label={node[Below]{Surface}}] 237 | ] 238 | [Hearer,edge label={node[Above]{Active}} 239 | [{$-i,-i$},edge label={node[Below]{Inverse}}] 240 | [{$x,x$},edge label={node[Below]{Surface}}] 241 | ] 242 | ] 243 | ] 244 | \end{forest} 245 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 246 | \end{figure} 247 | \end{frame} 248 | 249 | \begin{frame}[fragile] 250 | \frametitle{Matrix for when Nature chooses $\forall > \exists$} 251 | \begin{center} 252 | \begin{figure} 253 | \begin{tikzpicture} 254 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 255 | $x$&$-y$\\ 256 | $x$&$0$\\ 257 | $-i$&$x-p-i$\\ 258 | $-i$&$x-i$\\ 259 | }; 260 | \draw (m.north east) rectangle (m.south west); 261 | \draw (m.north) -- (m.south); 262 | \draw (m.east) -- (m.west); 263 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 264 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 265 | \node[above=5pt of a,anchor=base] {Active}; 266 | \node[above=5pt of b,anchor=base] {Passive}; 267 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 268 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 269 | \node[left=2pt of c,text width=1cm] {Surface}; 270 | \node[left=2pt of d,text width=1cm] {Inverse}; 271 | \node[above=18pt of m.north] (firm b) {Speaker}; 272 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 273 | \end{tikzpicture} 274 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 275 | \end{figure} 276 | \end{center} 277 | \end{frame} 278 | 279 | \begin{frame}[fragile] 280 | \frametitle{Matrix for when Nature chooses $\exists > \forall$} 281 | \begin{center} 282 | \begin{figure} 283 | \begin{tikzpicture} 284 | \matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) { 285 | $0$&$x-p$\\ 286 | $0$&$x$\\ 287 | $x-i$&$-p-i$\\ 288 | $x-i$&$-i$\\ 289 | }; 290 | \draw (m.north east) rectangle (m.south west); 291 | \draw (m.north) -- (m.south); 292 | \draw (m.east) -- (m.west); 293 | \coordinate (a) at ($(m.north west)!0.25!(m.north east)$); 294 | \coordinate (b) at ($(m.north west)!0.75!(m.north east)$); 295 | \node[above=5pt of a,anchor=base] {Active}; 296 | \node[above=5pt of b,anchor=base] {Passive}; 297 | \coordinate (c) at ($(m.north west)!0.25!(m.south west)$); 298 | \coordinate (d) at ($(m.north west)!0.75!(m.south west)$); 299 | \node[left=2pt of c,text width=1cm] {Surface}; 300 | \node[left=2pt of d,text width=1cm] {Inverse}; 301 | \node[above=18pt of m.north] (firm b) {Speaker}; 302 | \node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Hearer}; 303 | %\node[above=5pt of firm b] {If Nature chooses $\forall>\exists$ in a scrambling language}; 304 | \end{tikzpicture} 305 | \caption{Decision Flow of the Game of ``Everybody loves somebody''} 306 | \end{figure} 307 | \end{center} 308 | \end{frame} 309 | 310 | \begin{frame} 311 | \frametitle{Results and Intuitive Explanation}\pause 312 | 313 | \begin{itemize} 314 | \item \textbf{Passivization is a kind of signalling.} If a speaker passivizes, which is costly, \emph{he does it for a reason}, probably to get a more preferable quantifier order.\pause 315 | \begin{itemize} 316 | \item This kind of signalling make the passive sentences \emph{unambiguous}.\pause 317 | \end{itemize} 318 | \item If the speaker \emph{does not} passivize, there are two options for the Hearer to choose from:\pause 319 | \begin{itemize} 320 | \item Either the active sentence is already in the right order\ldots\pause 321 | \item or it is not, but the Speaker didn't want to accrue the passive penalty ($p$). 322 | \end{itemize} 323 | \end{itemize} 324 | 325 | \end{frame} 326 | 327 | \begin{frame} 328 | \frametitle{Scope in Scrambling Languages}\pause 329 | \begin{itemize} 330 | \item English has relatively rigid word order (subject-verb-object), but many languages have what is called `scrambling' which is free linear movement of nouns without the cost of transformations.\pause 331 | \item Scope is systematically different in languages like these.\pause 332 | \end{itemize} 333 | \begin{exe} 334 | \ex {\gll Har d\=aneshjui ye kit\=abi-ro mixune.\\ 335 | all student a book-OBJ reads\\ 336 | \trans{``Every student is reading a book.''}}\pause 337 | \ex {\gll Ye ket\=abi-ro har d\=aneshjui mixune.\\ 338 | a book-OBJ all student reads\\ 339 | \trans{``Every student is reading a book.''}} 340 | \end{exe}\pause 341 | \begin{itemize} 342 | \item However, both of these sentences \emph{must have} \textbf{surface scope}. They cannot be ambiguous. 343 | \end{itemize} 344 | \end{frame} 345 | 346 | \begin{frame} 347 | \frametitle{A Game Theoretic Account}\pause 348 | \begin{itemize} 349 | \item Given our previous suggested constraints, we can predict these scope availabilities.\pause 350 | \item Remember, \textbf{surface scope} is preferred and \textbf{transformations} are costly.\pause 351 | \item However, \textbf{scrambling} is not similarly costly{\ldots} so it's a new strategy. 352 | \end{itemize} 353 | \end{frame} 354 | 355 | \begin{frame} 356 | \begin{figure} 357 | \footnotesize 358 | \begin{forest} 359 | for tree={grow=east,draw=black,line width=0.2pt,parent anchor=east,child anchor=west,edge={draw=black},edge label={\Huge\color{black}},edge path={\noexpand\path[\forestoption{edge}](!u.parent anchor) -- ([xshift=-1.6cm].child anchor) -- 360 | (.child anchor)\forestoption{edge label}; 361 | }, 362 | l sep=2cm, 363 | } 364 | [Nature,rectangle, s sep=25pt, 365 | [Speaker,edge label={node[Below]{$\exists>\forall$}} 366 | [Hearer,edge label={node[Below]{Passive}} 367 | [{$-p-i,-p$},edge label={node[Below]{Inverse}}] 368 | [{$x-p,x$},edge label={node[Below]{Surface}}] 369 | ] 370 | [Hearer,edge label={node[Above]{Active}} 371 | [{$x-i,x-i$},edge label={node[Below]{Inverse}}] 372 | [{$0,0$},edge label={node[Below]{Surface}}] 373 | ] 374 | [Hearer, edge label={node[Above]{Scramble}} 375 | [{$-i,-i$}, edge label={node[Below]{Inverse}}] 376 | [{$x,x$}, edge label={node[Below]{Surface}}] 377 | ] 378 | ] 379 | [Speaker,edge label={node[Above]{$\forall>\exists$}} 380 | [Hearer,edge label={node[Below]{Passive}} 381 | [{$x-p-i,x-i$},edge label={node[Below]{Inverse}}] 382 | [{$-p,0$},edge label={node[Below]{Surface}}] 383 | ] 384 | [Hearer,edge label={node[Above]{Active}} 385 | [{$-i,-i$},edge label={node[Below]{Inverse}}] 386 | [{$x,x$},edge label={node[Below]{Surface}}] 387 | ] 388 | [Hearer, edge label={node[Above]{Scramble}} 389 | [{$x-i,x-i$}, edge label={node[Below]{Inverse}}] 390 | [{$0,0$}, edge label={node[Below]{Surface}}] 391 | ] 392 | ] 393 | ] 394 | \end{forest} 395 | \end{figure} 396 | \end{frame} 397 | 398 | \begin{frame} 399 | \frametitle{Optimal Strategies with Scrambling}\pause 400 | 401 | \begin{itemize} 402 | \item First, Scramble is a \textbf{dominant strategy} over Passivization.\pause 403 | \item Since there is no longer cost to reordering for the Speaker, the focal strategies are to use whatever strategy avoids the need for inverse scope.\pause 404 | \item Seeing this, the Hearer's best strategy should always be to assume \textbf{surface scope}.\pause 405 | \item Therefore, for each sentence (active or scrambled), there should only be only one unambiguous interpretation. 406 | \end{itemize} 407 | 408 | \end{frame} 409 | 410 | \begin{frame} 411 | \frametitle{Formal Terms}\pause 412 | 413 | \begin{itemize} 414 | \item In all situations, we narrow down scope possibilies with \emph{Schelling Points}/focal points.\pause 415 | \item The ``markedness'' of inverted scope or passivization are \emph{vital} to communication, as they signal the Speaker's intention and indirectly create the focal points. 416 | \end{itemize} 417 | 418 | \end{frame} 419 | 420 | \begin{frame} 421 | \frametitle{In an English-like language\ldots}\pause 422 | \begin{itemize} 423 | \item As assumed speakers \emph{want} to interpret quantifiers in linear order.\pause 424 | \item When a speaker produces a costly transformation (like a passive) the listener assumes that the new surface word order is the intended scope order.\pause 425 | \item If a speaker produces an untransformed sentence, the listener has two possible hypotheses: (1) the speaker intended surface scope, or (2) that the speaker intended inverse scope, but didn't want to undergo a costly transformation.\pause 426 | \item These two possibilities produce scope ambiguity. 427 | \end{itemize} 428 | \end{frame} 429 | 430 | 431 | \begin{frame} 432 | \frametitle{In Scrambling Languages}\pause 433 | \begin{itemize} 434 | \item In scrambling languages, since speakers have greater flexibility in ordering, listeners make different assumptions about intended scope.\pause 435 | \item If the speaker wants the object to scope over the subject, he can easily scramble it leftward.\pause 436 | \item Since he can do this, the unscrambled sentence has an unambiguous surface scope interpretation.\pause 437 | \item \textbf{Sidenote:} Potentially related, languages with scrambling/flexible word order, usually rely on things like passivization less often. 438 | \end{itemize} 439 | \end{frame} 440 | 441 | 442 | \begin{frame} 443 | \frametitle{Just a random difference?}\pause 444 | \begin{itemize} 445 | \item In addition to this correlation between rigid word-order and scrambling languages, we see that this theory still hold in rigid constructions in scrambling languages.\pause 446 | \item In Persian, for example, although nouns are flexible, negation must always be on the same part of a verb.\pause 447 | \item We should expect negative quantifiers to work similar to English sentences in that they produce ambiguity. This is the case:\pause 448 | \begin{exe} 449 | \ex {\gll Billy ye ket\=abi-ro na-xund.\\ 450 | Billy a book-OBJ not-read\\ 451 | \trans{``Billy didn't read a (particular) book.'' ($\exists>\neg$)or ``Billy didn't read any book.'' ($\neg>\exists$)}} 452 | \end{exe}\pause 453 | \item This holds in similar languages with scrambling and stable negation location (e.g. Korean). 454 | 455 | \end{itemize} 456 | \end{frame} 457 | 458 | \begin{frame} 459 | \frametitle{Rigidity = Ambiguity; Flexiblity = Unambiguousness}\pause 460 | 461 | \begin{itemize} 462 | \item The general theorem that arises from this analysis is that \emph{wherever} we have syntactic flexibility, we have ambiguity (and \textit{vice versa}.)\pause 463 | \item This difference, in agreement with our theory, is true \emph{across constructions}, not necessarily \emph{across languages}.\pause 464 | \item ``Scrambling'' languages are unambiguous in normal sentences, but are in more rigid constructions, ambiguity arises.\pause 465 | \begin{itemize} 466 | \item This is because the ambiguity is not a language-specific parameter, but a result of the strategies employable in any given context. 467 | \end{itemize} 468 | \end{itemize} 469 | 470 | \end{frame} 471 | 472 | \begin{frame} 473 | \frametitle{Local Rigidity}\pause 474 | In scrambling languages, generally we have syntactic flexibility accompanied by unambiguous surface scope.\pause 475 | 476 | \begin{exe} 477 | \ex \begin{xlist}\label{chin} 478 | \ex[]{\gll Meigeren dou zhuazou yige {n\"uren}.\\ 479 | everyone all arrest a woman\\ 480 | \trans{``Everyone arrested a woman.'' (${\forall}>{\exists} $)\label{chin1}}\pause 481 | } 482 | \ex[]{\gll (You) yige {n\"uren} meigeren dou zhuazou.\\ 483 | (have) a woman everyone all arrest.\\ 484 | \trans{``A woman was arrested by everyone.'' (${\exists}>{\forall}$)\label{chin2}} 485 | }\end{xlist} 486 | \end{exe}\pause 487 | 488 | But in syncactically inflexible constructions, ambiguity arises.\pause 489 | 490 | \begin{exe} 491 | \ex{ \begin{xlist} 492 | \ex[]{\gll Meigeren dou bei yige {n\"uren} zhuazou.\\ 493 | everyone all PASS a woman arrest\\ 494 | \trans{``Everyone was arrested by a woman.'' ($\forall > \exists$, ${\exists} > {\forall}$)\label{chin3}}\pause 495 | } 496 | \ex[*]{Bei yige {n\"uren} meigeren dou zhuazou.\\ 497 | PASS a woman everyone all arrest\\ 498 | \label{chin4} 499 | }\end{xlist}} 500 | \end{exe} 501 | \end{frame} 502 | 503 | \begin{frame} 504 | \frametitle{Local Rigidity in English as well}\pause 505 | 506 | English negation placement is \emph{rigid} with only one modal, as a result, the negation can take either wide or narrow scope.\pause 507 | 508 | \begin{exe} 509 | \ex Billy can not go. (${\forall}>{\exists}, {\exists}>{\forall}$)\pause 510 | \end{exe} 511 | 512 | On the other hand, where there are multiple modals, the negation can appear in multiple locations. This results in non-ambiguous sentences. (Note, the ambiguity is not with the \emph{could} modal, but \emph{have gone}.)\pause 513 | 514 | \begin{exe} 515 | \ex Billy could not have gone before we arrived.\label{could not}\pause 516 | \ex Billy could have not gone before we arrived.\label{have not} 517 | \end{exe} 518 | 519 | \end{frame} 520 | 521 | \begin{frame} 522 | \frametitle{But in languages where negation is \emph{always} flexible\ldots} 523 | 524 | {\ldots}like Chinese, we \emph{always} have a lack of ambiguity! 525 | 526 | \begin{exe} 527 | \ex {\gll Shujuan keyi \textbf{bu} gen Guorong {tiao wu}. \\ 528 | Shujuan may not with Guorong dace \\ 529 | \trans{``Shujuan is permitted not to dance with Guorong.'' ($may>{\neg}$)}} 530 | \ex {\gll Shujuan \textbf{bu} keyi gen Guorong {tiao wu}. \\ 531 | Shujuan not may with Guorong dance \\ 532 | \trans{``Shujuan can't dance with Guorong.'' (${\neg}>may$)}} 533 | \end{exe} 534 | 535 | \end{frame} 536 | 537 | \begin{frame} 538 | \frametitle{Empirical summary}\pause 539 | \centering 540 | 541 | \begin{tabular}{l|l} 542 | Rigid constructions & Flexible constructions\\\hline\pause 543 | English main clauses&Main clauses in scrambling languages\\\pause 544 | Persian negation&Chinese negation\\\pause 545 | English negation with auxes&English negation without auxes\\\pause 546 | Chinese passives&English Passives*\\\pause 547 | \textbf{All of these are ambiguous.}&\textbf{All of these are non-ambiguous.} 548 | \end{tabular} 549 | \end{frame} 550 | 551 | \begin{frame} 552 | \frametitle{The General Theory}\pause 553 | 554 | \begin{itemize} 555 | \item Quantifier scope interpretaions are not so much syntactically \emph{licensed} so much as they are \textbf{pruned} from the all possible combinations of scopes ($q!$ where $q=$ number of quantifiers).\pause 556 | \begin{itemize} 557 | \item That is, \emph{all} quantifier scope interpretations are possible in the abstract (hence Chomsky's aphasia)\ldots\pause 558 | \item but the pragmatics of the structure of a language (what other constructions we have available) determine what are actually plausible interpretations.\pause 559 | \end{itemize} 560 | 561 | \item Without any syntactic machinery, we have already done a lot of the work of narrowing in on what interpretations are possible.\pause 562 | \item But the story is not done yet! 563 | \end{itemize} 564 | \end{frame} 565 | 566 | \begin{frame} 567 | \frametitle{Project Extension}\pause 568 | \begin{itemize} 569 | \item Replace generative notions of syntactically-determined quantifier scope ambiguities with more plausible, externally-driven factors.\pause 570 | \item Unify this account with other scope alternations (say, the unavailability of semantically implausible scope interpretations) into a general theory of scope where possible interpretations are \emph{pruned}, rather than derived by some syntactic engine.\pause 571 | \item Similar accounts for related phenomena? C-command? Cross-over? 572 | \item Extensive Game Theory w.r.t different quantifiers and remodelling given data. 573 | \end{itemize} 574 | \end{frame} 575 | 576 | \begin{frame} 577 | \frametitle{The End} 578 | \begin{center} 579 | %\includegraphics[height=.85\textheight]{toon.png} 580 | \end{center} 581 | 582 | \end{frame} 583 | 584 | \end{document} 585 | --------------------------------------------------------------------------------