scalimp_inference.tex

   1 \documentclass[a4paper,russian]{article}
   2
   3 \usepackage[koi8-r]{inputenc}
   4 \usepackage{babel}
   5 \usepackage{url}
   6
   7 \newcommand*{\axiom}[1]{\textsc{#1}} % The style to use when I refer
   8                                 % to an "axiom".
   9 \newcommand*{\axiomIntro}[1]{\introStyle{\axiom{#1}}} % The style to use
  10                                 % when I introduce an "axiom" in my text
  11                                 % for the first time. (Bold to make it
  12                                 % easily discoverable in the text.)
  13 \newcommand*{\introStyle}[1]{\textbf{#1}} % For other cases of
  14                                 % introducing a key concept, but not as
  15                                 % formal as an axiom.
  16
  17 \author{é×ÁÎ úÁÈÁÒØÑÝÅ× \url!<imz@altlinux.org>!}
  18 \title{æÏÒÍÁÌÉÚÕÅÍ ×Ù×ÏÄ Gricean implicatures. úÁÞÅÍ ÎÕÖÎÙ
  19   \axiom{opinionated speaker} É \axiom{informed speaker}?}
  20 \date{10~ÄÅËÁÂÒÑ 2005~Ç. (Ó ÍÁÌÙÍÉ ÐÒÁ×ËÁÍÉ ÏÔ~\today)}
  21
  22 \usepackage{amsmath}
  23 \usepackage{amssymb}
  24
  25 %\usepackage{mathpartir} % Do I want to draw the horizontal lines in
  26 % the derivations, as usual in logic, or just write it with a word?
  27 % A word must be more understandable by anyone...
  28 \newcommand*{\inferrule}[2]{%\samepage
  29   \begin{gather}
  30     \notag
  31     #1\qquad \text{ \textsf{--- ×Ù×ÏÄ:}}% Applying an automatic
  32                                 % derivation rule; logicians usually
  33                                 % use a horizontal line here.
  34     \\
  35     #2
  36   \end{gather}}
  37
  38 \newcommand*{\iref}[1]{\eqref{#1}\colon}
  39
  40 %\newcommand*{\assert}{.}
  41 %\DeclareMathOp{\assert}{.}
  42
  43 \newcommand*{\Cimplies}{\rightarrow}
  44 \newcommand*{\Cnot}{\neg}
  45 \newcommand*{\Cor}{\vee}
  46 \newcommand*{\Cand}{\wedge}
  47
  48 \newcommand*{\Pn}[1]{P_{#1}}
  49 \newcommand*{\Pa}{\Pn{a}}
  50 \newcommand*{\Pb}{\Pn{b}}
  51 \newcommand*{\Pc}{\Pn{c}}
  52
  53 %\newcommand*{\said}[1]{[(#1)]}
  54 %\newcommand*{\said}[1]{[[#1]]}
  55 %\newcommand*{\said}[1]{[#1*]}
  56 %\newcommand*{\said}[1]{\blacksquare_{#1}}
  57 \newcommand*{\said}[1]{\boxtimes_{#1}}
  58
  59
  60 \begin{document}
  61 \maketitle
  62
  63 ðÒÉÍÅÒ:
  64 \begin{equation*}
  65   \label{eq:example}
  66   \text{Many of your students complained.}
  67 \end{equation*}
  68
  69 alternatives (or, competitors):
  70 $\{\text{a. some}, \text{b. many},\text{c. all}\}$.
  71
  72
  73 \section{òÁÓÓËÁÚ}
  74 \label{sec:story}
  75
  76
  77 üÔÏ ×Ó£ ËÁË-ÔÏ ÔÏÎËÏ É ÎÅ ÏÞÅÎØ ÕÂÅÄÉÔÅÌØÎÏ ÎÁ ÍÏÊ ×ÚÇÌÑÄ. ÷ÏÔ ÔÁËÁÑ
  78 ÓÈÅÍÁ (ÉÚÌÏÖÅÎÉÅ ÐÏÓÌÅ ÐÒÏÞÔÅÎÉÑ \cite[ÓÔÒ. 2--3]{KvFCourse}).
  79
  80 \paragraph{îÅËÏÔÏÒÙÅ ÏÂÏÚÎÁÞÅÎÉÑ.}
  81 ðÕÓÔØ $S$~--- the speaker, ÆÏÒÍÕÌÁ $[S]P$ ÉÍÅÅÔ ÓÍÙÓÌ <<$S$ ÓÞÉÔÁÅÔ,
  82 ÞÔÏ $P$>>, $\said{S} P$~--- <<$S$ ÓËÁÚÁÌ $P$>>,
  83 \begin{align*}
  84 \Pa &\text{--- some of your students complained}\\
  85 \Pb &\text{--- many of your students complained}\\
  86 \Pc &\text{--- all of your students complained}\\
  87 \end{align*}
  88
  89 \paragraph{âÙÓÔÒÙÊ ÏÔ×ÅÔ.} ðÕÓÔØ $S$ ÓËÁÚÁÌ $\Pb$.
  90 ðÒÅÄÐÏÌÏÖÅÎÉÅ \axiom{opinionated speaker}
  91 ÎÕÖÎÏ ÚÁÔÅÍ, ÞÔÏÂÙ × ×Ù×ÏÄÁÈ ÉÍÐÌÉËÁÔÕÒ (ËÁËÉÈ?) ÐÒÏÄ×ÉÎÕÔØÓÑ ÄÁÌØÛÅ
  92 ×Ù×ÅÄÅÎÎÏÇÏ ÉÚ ÐÒÉÎÃÉÐÏ× ÒÁÚÇÏ×ÏÒÁ $\iref{eq:not-believes-c} \Cnot[S] \Pc$.
  93
  94
  95 \paragraph{æÁËÔ~--- illocutionary act.}
  96 æÁËÔ: $S$ ÓËÁÚÁÌ $\Pb$
  97 %
  98 \begin{equation}
  99   \label{eq:act}
 100 %  \text{$S$ ÓËÁÚÁÌ $P_b$}
 101   \said{S} \Pb
 102   \tag{0}
 103 \end{equation}
 104
 105
 106 \paragraph{Illocutionary force.}\footnote{üÔÏÔ ÐÁÒÁÇÒÁÆ ÎÅ ÉÍÅÅÔ
 107   ÏÔÎÏÛÅÎÉÑ Ë ×ÙÞÉÓÌÅÎÉÀ ÉÍÐÌÉËÁÔÕÒ~--- ÏÓÎÏ×ÎÏÊ ÔÅÍÅ ÒÁÓÓËÁÚÁ, ÎÏ
 108   ÐÏËÁÚÙ×ÁÅÔ, ËÁË ÏÂÒÁÂÙÔÙ×ÁÅÔÓÑ ÏÓÎÏ×ÎÏÅ ÚÎÁÞÅÎÉÅ. íÏÖÎÏ ÐÏÔÏÍ
 109   ÓÒÁ×ÎÉÔØ Ó ÉÍÐÌÉËÁÔÕÒÁÍÉ.}
 110
 111 õÔ×ÅÒÄÉÔÅÌØÎÁÑ ``illocutionary force'' ÜÔÏÇÏ ÁËÔÁ:
 112 $S$ ÚÁÓÔÁ×ÌÑÅÔ ÎÁÓ ÓÞÉÔÁÔØ, ÞÔÏ $\Pb$:%
 113 \footnote{äÏÐÕÓËÁÅÍ ÄÅÊÓÔ×ÉÅ \axiomIntro{ÕÔ×ÅÒÄÉÔÅÌØÎÏÊ illocutionary force}:
 114   \begin{equation*}
 115     \said{S} P \Cimplies P.
 116   \end{equation*}
 117   ÷ ÞÁÓÔÎÏÓÔÉ (ÐÏÄÓÔÁ×ÌÑÑ~$\Pb$ ×ÍÅÓÔÏ~$P$ × ÜÔÕ <<ÓÈÅÍÕ-ÁËÓÉÏÍÕ>>),
 118   \begin{equation}
 119     \label{eq:force-b}
 120     \said{S} \Pb \Cimplies \Pb.
 121   \end{equation}
 122   \inferrule{\iref{eq:act} \said{S} \Pb ,\quad
 123     \iref{eq:force-b} \said{S} \Pb \Cimplies \Pb}
 124   {\Pb\tag{\ref{eq:content}}}}
 125 %
 126 \begin{equation}
 127   \label{eq:content}
 128   \Pb
 129   %\tag{#1}
 130 \end{equation}
 131
 132 \paragraph{ðÒÉÎÃÉÐÙ ÒÁÚÇÏ×ÏÒÁ, ÞÔÏ-ÔÏ × ÓÔÉÌÅ Gricean/Gamut inference.}%
 133 \footnote{íÅÈÁÎÉÚÍ, ÐÒÅÄÓÔÁ×ÌÅÎÎÙÊ ÔÕÔ, ÍÏÖÅÔ, ÎÅ ÏÞÅÎØ
 134   ×ÎÕÔÒÅÎÎÅ ÐÏÓÌÅÄÏ×ÁÔÅÌÅÎ, ÎÏ ÄÏ×ÏÌØÎÏ ÐÒÏÓÔ. ïÎ ÓÌÕÖÉÔ ÄÌÑ ÄÅÍÏÎÓÔÒÁÃÉÉ ÉÄÅÉ Ï
 135   ÅÓÔÅÓÔ×ÅÎÎÏÓÔÉ ÐÏÌÕÞÅÎÉÑ ÉÍÅÎÎÏ ×Ù×ÏÄÁ~\eqref{eq:not-believes-c} ×
 136   ÔÁËÉÈ ÓÉÓÔÅÍÁÈ É ÏÔ×ÅÔÁ ÎÁ ×ÏÐÒÏÓ, ÚÁÞÅÍ ÎÕÖÎÏ ÐÒÅÄÐÏÌÏÖÅÎÉÅ
 137   \axiom{opinionated speaker}.}
 138
 139 \emph{some} ÐÏÐÁÄÁÅÔ × ÔÁËÏÊ ÎÁÂÏÒ \introStyle{alternatives}/competitors:
 140 $\lbrace\text{a. some}, \text{b. many},
 141 \text{c. all}\rbrace$. áÌØÔÅÒÎÁÔÉ×ÎÙÅ ×ÙÓËÁÚÙ×ÁÎÉÑ: $\Pa$, $\Pb$,
 142 $\Pc$, ÐÒÉÞ£Í, × ÓÏÏÔ×ÅÔÓÔ×ÉÉ Ó ÉÈ ÓÅÍÁÎÔÉËÏÊ,
 143 \begin{align}
 144 \label{eq:strength}
 145 \Pc &\Cimplies \Pb, &\Pb &\Cimplies \Pa.
 146 \end{align}
 147
 148 ïÂÏÚÎÁÞÅÎÉÅ: ÆÏÒÍÕÌÁ $\Diamond R$ ÉÍÅÅÔ ÓÍÙÓÌ <<ÐÏÚ×ÏÌÅÎÏ $R$>>.
 149
 150 \introStyle{ðÒÁ×ÉÌÁ ÒÁÚÇÏ×ÏÒÁ} (ÉÌÉ ÅÝ£ ÞÔÏ-ÔÏ) ÏÐÒÅÄÅÌÑÀÔ ÕÓÌÏ×ÉÑ ÔÏÇÏ, ÞÔÏ $S$
 151 ÐÏÚ×ÏÌÅÎÏ ÓËÁÚÁÔØ $P$:
 152 %(in a position to say $P$):
 153 \begin{equation}\label{eq:in-a-pos}
 154   (\Diamond \said{S} P) \leftrightarrow ( ([S] P) \Cand \dotsb )
 155 \end{equation}
 156 (ÎÁ ÍÅÓÔÅ <<$\dotsb$>> ÅÝ£ ËÁËÉÅ-ÔÏ ÕÓÌÏ×ÉÑ, ËÏÔÏÒÙÅ ÎÁÍ ÎÅ ×ÁÖÎÙ;
 157 ÐÕÓÔØ ÏÎÉ ×ÓÅÇÄÁ ×ÙÐÏÌÎÅÎÙ; ÂÅÚ ÕÞ£ÔÁ <<$\dotsb$>> ÜÔÏ ÐÏÈÏÖÅ ÎÁ quality maxim).
 158
 159 ðÒÅÄÐÏÌÁÇÁÅÍ pragmatic \axiomIntro{correctness}, Á ÉÍÅÎÎÏ, ÞÔÏ <<ÐÏ×ÅÄÅÎÉÅ
 160 ÐÒÏÉÓÈÏÄÉÔ × ÒÁÍËÁÈ ÄÏÚ×ÏÌÅÎÎÏÇÏ>>:
 161 \begin{equation*}
 162   R \Cimplies \Diamond R,
 163 \end{equation*}
 164 É ÞÔÏ ×ÙÐÏÌÎÑÔÓÑ \axiomIntro{quantity maxim}:
 165 \begin{align*}
 166   \said{S} P
 167   &\Cimplies ( (\Diamond \said{S} Q) \Cimplies (P \Cimplies  Q))
 168   &&\text{ÄÌÑ ÌÀÂÏÇÏ $Q$~--- ÁÌØÔÅÒÎÁÔÉ×Ù $P$}
 169 \end{align*}
 170 ($S$ ÄÏÌÖÅÎ ÂÙÌ ÓËÁÚÁÔØ ÁÌØÔÅÒÎÁÔÉ×Õ, ÄÁÀÝÕÀ ÂÏÌØÛÅ ×ÓÅÇÏ ÉÎÆÏÒÍÁÃÉÉ =
 171 ÎÁÉÂÏÌÅÅ ÓÉÌØÎÕÀ; ËÏÎÅÞÎÏ, ÉÚ ÔÅÈ, ËÏÔÏÒÙÅ ÐÏÚ×ÏÌÅÎÏ ÓËÁÚÁÔØ).
 172
 173 ÷ ÞÁÓÔÎÏÓÔÉ, × ÎÁÛÅÍ ÐÒÉÍÅÒÅ (ÐÏÄÓÔÁ×ÌÑÑ ËÏÎËÒÅÔÎÙÅ ÕÔ×ÅÒÖÄÅÎÉÑ × ÜÔÉ Ä×Å <<ÓÈÅÍÙ-ÁËÓÉÏÍÙ>>):
 174 %(ÎÅ ÂÕÄÅÍ ÏÂÒÁÝÁÔØ ×ÎÉÍÁÎÉÅ ÎÁ ÄÒÕÇÉÅ ÎÅÏÂÈÏÄÉÍÙÅ ÕÓÌÏ×ÉÑ, ËÒÏÍÅ ÕËÁÚÁÎÎÏÇÏ):
 175 \begin{align}
 176   \label{eq:in-a-position-b}
 177   \said{S}\Pb &\Cimplies \Diamond \said{S}\Pb\\
 178   \label{eq:b-to-a}
 179   \said{S}\Pb &\Cimplies ( \Diamond \said{S}\Pa \Cimplies (\Pb \Cimplies \Pa))\\
 180   \label{eq:b-to-c}
 181   \said{S}\Pb &\Cimplies ( \Diamond \said{S}\Pc \Cimplies (\Pb \Cimplies \Pc))
 182 \end{align}
 183
 184 %inference (ËÁË Õ Grice/Gamut):
 185
 186 \inferrule{
 187   \iref{eq:act}\said{S}\Pb,\quad
 188   \iref{eq:strength} \Pc \Cimplies \Pb,\quad
 189   \eqref{eq:b-to-c}}
 190 {\label{eq:not-in-a-position-c}
 191   \Cnot \Diamond \said{S}\Pc}
 192
 193 \inferrule{
 194   \eqref{eq:not-in-a-position-c},\quad \eqref{eq:in-a-pos}}
 195 {\label{eq:not-believes-c}
 196   \Cnot [S]\Pc}
 197
 198 üÔÏ ÏÞÅÎØ ÓÌÁÂÏÅ ÚÁËÌÀÞÅÎÉÅ; × ÏÂÌÁÓÔØ ÔÏÇÏ, ÞÔÏ ÍÙ ÄÏÌÖÎÙ ÓÞÉÔÁÔØ
 199 ×ÅÒÎÙÍ, ÎÅ ÐÏÐÁÄÁÅÔ ÎÉÞÅÇÏ ÐÒÏ ×ÅÒÎÏÓÔØ/ÎÅ×ÅÒÎÏÓÔØ
 200 $\Pc$.\footnote{<<ïÂÌÁÓÔØ ÔÏÇÏ, ÞÔÏ ÍÙ ÄÏÌÖÎÙ ÓÞÉÔÁÔØ ×ÅÒÎÙÍ>>~---
 201   ÜÔÏ ËÁË ÒÁÚ ÎÁÛÉ ×Ù×ÏÄÙ, ÐÒÅÄÓÔÁ×ÌÅÎÎÙÅ ÚÄÅÓØ ÎÕÍÅÒÏ×ÁÎÎÙÍÉ
 202   ÆÏÒÍÕÌÁÍÉ; ÄÅÊÓÔ×ÉÅ ÞØÅÇÏ-ÔÏ ×ÙÓËÁÚÙ×ÁÎÉÑ ÎÁ ÎÁÓ-ÓÌÕÛÁÀÝÉÈ~--- ÜÔÏ
 203   ÐÏÐÁÄÁÎÉÅ ËÁËÉÈ-ÔÏ ÎÏ×ÙÈ ÕÔ×ÅÒÖÄÅÎÉÊ × ÜÔÕ <<ÏÂÌÁÓÔØ>>. ÷ ÜÔÏÍ
 204   ÒÁÓÓËÁÚÅ ÐÒÅÄÌÁÇÁÅÔÓÑ ÏÄÉÎ ÁÎÁÌÉÚ, ÐÏÞÅÍÕ ÜÔÏ ÄÅÊÓÔ×ÉÅ ÔÁËÏÅ, ËÁËÏÅ
 205   ÎÁÂÌÀÄÁÅÔÓÑ ÎÁ ÓÁÍÏÍ ÄÅÌÅ; Á ÉÍÅÎÎÏ, ÐÏÞÅÍÕ ×ÙÓËÁÚÁÎÎÏÅ~$\Pb$
 206   ÄÏÌÖÎÏ ÚÁÓÔÁ×ÌÑÔØ ÎÁÓ-ÓÌÕÛÁÀÝÉÈ ÄÅÌÁÔØ ×Ù×ÏÄ, ÞÔÏ~$\Cnot\Pc$~--- ÔÏ, ÞÔÏ,
 207   É ÎÁÂÌÀÄÁÅÔÓÑ ÎÁ ÓÁÍÏÍ ÄÅÌÅ ÐÒÉ ÏÂÝÅÎÉÉ,
 208   ËÁË ÓÞÉÔÁÅÔÓÑ ÌÉÎÇ×ÉÓÔÁÍÉ.}
 209
 210 \paragraph{Opinionated speaker.}
 211 îÁ ÜÔÏÍ ÐÒÉÛÌÏÓØ ÂÙ ÏÓÔÁÎÏ×ÉÔØÓÑ. îÏ ÐÒÅÄÐÏÌÁÇÁÅÍ \axiomIntro{opinionated
 212  speaker}:
 213 \begin{align*}
 214   ([S]P) &\Cor ([S] \Cnot P) &&\text{ÄÌÑ ÌÀÂÏÇÏ $P$}
 215 \end{align*}
 216 ÷ ÞÁÓÔÎÏÓÔÉ (ÐÏÄÓÔÁ×ÌÑÑ~$\Pc$ ×ÍÅÓÔÏ~$P$ × ÜÔÕ <<ÓÈÅÍÕ-ÁËÓÉÏÍÕ>>),
 217 \begin{equation}
 218   \label{eq:op-speaker-c}
 219   ([S]\Pc) \Cor ([S] \Cnot \Pc).
 220 \end{equation}
 221
 222 \inferrule{
 223 \iref{eq:not-believes-c} \Cnot ([S]\Pc),\quad \eqref{eq:op-speaker-c}}
 224 {[S] \Cnot \Pc \label{eq:believes-not-c}}
 225
 226 \paragraph{``A Final Step (if so desired)'' \cite{KvFCourse}.}
 227 îÁ ÜÔÏÍ ÐÒÉÛÌÏÓØ ÂÙ ÏÓÔÁÎÏ×ÉÔØÓÑ.
 228 îÏ ÐÒÅÄÐÏÌÁÇÁÅÍ \axiomIntro{informed speaker}:
 229 \begin{align*}
 230   ([S]P) &\Cimplies P && \text{ÄÌÑ ÌÀÂÏÇÏ ÒÅÌÅ×ÁÎÔÎÏÇÏ $P$}
 231 \end{align*}
 232
 233 ÷ ÞÁÓÔÎÏÓÔÉ (ÐÏÄÓÔÁ×ÌÑÑ~$\Pc$ ×ÍÅÓÔÏ~$P$ × ÜÔÕ <<ÓÈÅÍÕ-ÁËÓÉÏÍÕ>>),
 234 \begin{equation}
 235   \label{eq:informed-c}
 236   ([S]\Cnot \Pc) \Cimplies \Pc
 237 \end{equation}
 238
 239 \inferrule{\eqref{eq:believes-not-c},\quad \eqref{eq:informed-c}}
 240 {\Cnot \Pc \label{eq:not-c}}
 241
 242 (äÌÑ $\Pa$ ×Ó£ ÔÁË ÖÅ ÎÅ ÒÁÂÏÔÁÅÔ, ÐÏÔÏÍÕ ÞÔÏ ÏÎÏ ÓÌÁÂÅÅ $\Pb$.)
 243
 244 \paragraph{éÔÏÇÉ.}
 245 ôÁËÉÍ ÏÂÒÁÚÏÍ, illocutionary force ÚÁÓÔÁ×ÌÑÅÔ ÎÁc ÐÒÉÎÑÔØ $\Pb$,
 246 pragmatic inference ÉÚ \eqref{eq:act} ÄÁ£Ô ÉÍÐÌÉËÁÔÕÒÕ $\Cnot\Pc$.
 247
 248 íÏÖÎÏ ÂÙÌÏ ÂÙ ÒÁÚÌÏÖÉÔØ illocutionary force ÎÁ ÔÅ ÖÅ ÐÒÉÎÃÉÐÙ,
 249 Á ÉÍÅÎÎÏ ÉÚ $\said{S} \Pb$ ×Ù×ÏÄÉÍ $[S] \Pb$,
 250 É ÉÚ $[S] \Pb$ É \axiom{informed speaker}: $\Pb$.
 251
 252 ÷ÏÔ ÔÁËÏÅ ÍÏ£ ÉÚÌÏÖÅÎÉÅ, Ñ ÓÍÏÔÒÅÌ \cite[ÓÔÒ. 2--3]{KvFCourse}.
 253
 254
 255 \begin{thebibliography}{}
 256
 257 \bibitem[KvF course]{KvFCourse}  Kai von Fintel's course on Pragmatics
 258   at LSA summer institute 2005. The handouts were at
 259   \url!http://semantics-online.org/lsa311/lsa311-ho-2.pdf!.
 260
 261 \end{thebibliography}
 262
 263 \end{document}
 264
 265 %%% Local Variables:
 266 %%% mode: latex
 267 %%% TeX-master: t
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