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dialrules.tex
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\chapter{Dialogue rules}
\label{app:dialrules}
\section{Universal resources}
\subsection{Types of Information States}
\label{app:infostate}
\textit{InfoState} (Chapter~\ref{ch:infex})
\smallrecord{\smalltfield{private}{\smallrecord{\smalltfield{agenda}{[\textit{MoveType}(\textit{SELF})]}}} \\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smalltfield{move}{\textit{Move}(\textit{SELF})} \\
\smalltfield{chart}{\textit{Chart}}
\\
\smalltfield{e}{m-interp(chart,move)}}$\vee$\textit{ERec}}\\
\smalltfield{commitments}{\textit{RecType}}}}}
[??We need other options than \textit{SELF}]
\textit{InitInfoState} (Chapter~\ref{ch:infex})
The type of initial or empty information states
\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{[]}{[\textit{RecType}]}}} \\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\textit{ERec}}\\
\smallmfield{commitments}{\textit{Rec}}{\textit{RecType}}}}}
\textit{GameBoard} (Chapter~\ref{ch:propnames})
$T$ : \textit{GameBoard} iff $T\sqsubseteq$ \textit{InfoState}
\textit{TotalInfoState} (Chapter~\ref{ch:propnames})
\record{\tfield{ltm}{\textit{RecType}} \\
\tfield{gb}{(ltm$\rightarrow$\textit{GameBoard})}}
\subsection{Action functions}
\label{app:actfuns}
\paragraph{Licensing conditions on type acts}
If
$f:(T\rightarrow\textit{Type})$ is an action function then for any
object $a$ and agent $A$, $a:_A T$ licenses $:_A f(a)!$
\textit{de se}: If
$f:(T\rightarrow(\textit{Ind}\rightarrow\textit{Type}))$ is an action function then for any
object $a$ and agent $A$, $a:_A T$ licenses $:_A f(a)(A)!$
\paragraph{ExecTopAgenda} (Chapter~\ref{ch:infex})
$\lambda
r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{RecType}]}}}} \hspace*{.5em}.
\\
\hspace*{2em}\record{\tfield{move}{fst($r$.private.agenda)} \\
\tfield{chart}{\textit{Chart}} \\
\tfield{e}{m-interp(chart,move)}}
\subsection{Perception functions (type shifts)}
\paragraph{Licensing conditions on type acts}
If
$f:(T\rightarrow\textit{Type})$ is a perception function then for any
object $o$ and agent $A$, $o:_A T$ licenses $o:_A f(o)$
\textit{de se}: If
$f:(T\rightarrow(\textit{Ind}\rightarrow\textit{Type}))$ is a perception function then for any
object $o$ and agent $A$, $o:_A T$ licenses $o:_A f(o)(A)$
\textbf{PerceiveSpeechAct}($T$), $T$$\sqsubseteq$\textit{Phon}\ \ \ (Chapter~\ref{ch:infex})
$\lambda e$:\smallrecord{\smalltfield{e}{$T$} \\
\smallmfield{au}{\textit{SELF}}{\textit{Ind}}}. \\
\hspace*{2em}\record{\tfield{move}{\record{\tfield{e}{\textit{SpeechAct}
\d{$\wedge$}
\smallrecord{\smallmfield{au}{\textit{SELF}}{\textit{Ind}}}}
\\
\tfield{cnt}{\textit{Cnt}}
\\
\tfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}}}
\\
\tfield{chart}{$\mathfrak{C}_T$} \\
\tfield{e}{m-interp(chart,move)}}
where $\mathfrak{C}_T$ is the type of charts assigned to utterances of
type $T$ (as a result of parsing). In Chapter~\ref{ch:infex}
$\mathfrak{C}_T$ is equated with $\Sigma_T$, the type of signs
associated with utterances of type $T$.
\subsection{Update functions}
\label{app:updatefuns}
\paragraph{Licensing conditions on type acts}
If $f:(T_1\rightarrow(T_2\rightarrow\textit{Type}))$ is an update
function, $A$ is an agent, $s_i$ is $A$'s current information state,
$s_i:_A T_i$, $T_i\sqsubseteq T_1$ (and $s_i:T_1$), then an event $e:_A
T_2$ (and $e:T_2$) licenses $s_{i+1}:_A T_i$ \fbox{\d{$\wedge$}}
$f(s_i)(e)$.
%\samepage{
\paragraph{IntegrateOwnAssertion} (Chapter~\ref{ch:infex})
%\nopagebreak
% \hspace*{-3em}\begin{minipage}{\textwidth}
$\lambda
r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{MoveType}(\textit{SELF})]}}}}
\\
\hspace*{1em}$\lambda
u$:\record{\tfield{move}{fst($r$.private.agenda)
\d{$\wedge$}
\smallrecord{\smalltfield{e}{\smallrecord{\smallmfield{sp}{\textit{SELF}}{\textit{Ind}}
\\
\smalltfield{au}{\textit{Ind}}}}}
\d{$\wedge$}
\smallrecord{\smalltfield{e}{\textit{Assertion}}}} \\
\tfield{chart}{\textit{Chart}} \\
\tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
\hspace*{2em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{\begin{tabular}{l}
\smallrecord{\smalltfield{e}{\textit{Acknowledgement}\d{$\wedge$}\smallrecord{\smallmfield{sp}{$u$.move.e.au}{\textit{Ind}}
\\
\smallmfield{au}{\textit{SELF}}{\textit{Ind}}}}
\\
\smallmfield{cnt}{$u$.move.cnt}{\textit{RecType}} \\
\smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}} \\
\hspace*{10em}$\mid$ rst($r$.private.agenda) \end{tabular}}{[\textit{MoveType}(\textit{SELF})]}}}
\\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}(\textit{SELF})} \\
\smallmfield{chart}{$u$.chart}{\textit{Chart}}
\\
\smallmfield{e}{$u$.e}{m-interp(chart,move)}}}}}}
% \end{minipage}
% $\lambda
% r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{RecType}]}}}}
% \\
% \hspace*{2em}$\lambda u$:\record{\tfield{move}{fst($r$.private.agenda)$\wedge$\smallrecord{\smallmfield{i-force}{assert}{\textit{IForce}}}} \\
% \tfield{chart}{\textit{Chart}} \\
% \tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
% \hspace*{4em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{rst($r$.private.agenda)}{[\textit{RecType}]}}}
% \\
% \smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
% \smallmfield{chart}{$u$.chart}{\textit{Chart}}
% \\
% \smallmfield{e}{$u$.e}{m-interp(chart,move)}}}}}}
%}
%\pagebreak
\paragraph{IntegrateOtherAssertion} (Chapter~\ref{ch:infex})\nopagebreak
$\lambda
r$:\record{\tfield{private}{\record{\tfield{agenda}{[\textit{RecType}]}}}}
\\
\hspace*{1em}$\lambda
u$:\smallrecord{\smalltfield{move}{\smallrecord{\smalltfield{e}{\textit{Assertion}\d{$\wedge$}\smallrecord{\smalltfield{sp}{\textit{Ind}} \\
\smallmfield{au}{\textit{SELF}}{\textit{Ind}}}}
\\
\smalltfield{cnt}{\textit{RecType}}
\\
\smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}}}
\\
\smalltfield{chart}{\textit{Chart}} \\
\smalltfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
\hspace*{3em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{\begin{tabular}{l}\smallrecord{\smalltfield{e}{\textit{Acknowledgement}
\d{$\wedge$}\smallrecord{\smallmfield{sp}{\textit{SELF}}{\textit{Ind}} \\
\smallmfield{au}{$u$.move.e.sp}{\textit{Ind}}}}
\\
\smallmfield{cnt}{$u$.move.cnt}{\textit{RecType}}
\\
\smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}} \\
\hspace*{12em}$|\ r$.private.agenda\end{tabular}}{[\textit{RecType}]}}}
\\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
\smallmfield{chart}{$u$.chart}{\textit{Chart}}
\\
\smallmfield{e}{$u$.e}{m-interp(chart,move)}}
}}}}
%\nopagebreak
% $\lambda
% r$:\record{\tfield{private}{\record{\tfield{agenda}{[\textit{RecType}]}}}}
% \\
% \hspace*{1em}$\lambda
% u$:\smallrecord{\smalltfield{move}{\smallrecord{\smalltfield{e}{\textit{Assertion}} \\
% \smalltfield{c$_{\mathrm{SELF}}$}{addressed(e,SELF)}
% \\
% \smalltfield{cnt}{\textit{RecType}}
% \\
% \smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}}}
% \\
% \smalltfield{chart}{\textit{Chart}} \\
% \smalltfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
% \hspace*{3em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{\begin{tabular}{l}\smallrecord{\smalltfield{e}{\textit{Acknowledgement}} \\
% \smalltfield{c$_{\mathrm{SELF}}$}{actor(e,SELF)}
% \\
% \smallmfield{cnt}{$u$.move.cnt}{\textit{RecType}}
% \\
% \smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}}
% $|\ r$.private.agenda\end{tabular}}{[\textit{RecType}]}}}
% \\
% \smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
% \smallmfield{chart}{$u$.chart}{\textit{Chart}}
% \\
% \smallmfield{e}{$u$.e}{m-interp(chart,move)}}
% }}}}
%}
\paragraph{IntegrateOwnAcknowledgement} (Chapter~\ref{ch:infex})
\nopagebreak
$\lambda
r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{RecType}]}}}\\
\tfield{shared}{\record{\tfield{latest-utterance}{
\record{\tfield{move}{
\record{\tfield{content}{\textit{RecType}}}}}}
\\
\tfield{commitments}{\textit{RecType}}}}}
\\
\hspace*{1em}$\lambda
u$:\record{\tfield{move}{fst($r$.private.agenda)\d{$\wedge$}\smallrecord{
\smalltfield{e}{\textit{Acknowledgement}}}\d{$\wedge$}\smallrecord{\smalltfield{e}{\smallrecord{\smallmfield{sp}{\textit{SELF}}{\textit{Ind}}}}}
} \\
\tfield{chart}{\textit{Chart}} \\
\tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
\hspace*{2em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{rst($r$.private.agenda)}{[\textit{RecType}]}}}
\\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
\smallmfield{chart}{$u$.chart}{\textit{Chart}}
\\
\smallmfield{e}{$u$.e}{m-interp(chart,move)}}}
\\
\smallmfield{commitments}{\smallrecord{\smalltfield{prev}{$r$.commitments}}\d{$\wedge$}$u$.move.cnt}{\textit{RecType}}}}}
% $\lambda
% r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{RecType}]}}}\\
% \tfield{shared}{\record{\tfield{latest-utterance}{
% \record{\tfield{move}{
% \record{\tfield{content}{\textit{RecType}}}}}}
% \\
% \tfield{commitments}{\textit{RecType}}}}}
% \\
% \hspace*{2em}$\lambda
% u$:\record{\tfield{move}{fst($r$.private.agenda)$\wedge$\smallrecord{
% \smalltfield{e}{\textit{Acknowledgement}}}
% } \\
% \tfield{chart}{\textit{Chart}} \\
% \tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
% \hspace*{4em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{rst($r$.private.agenda)}{[\textit{RecType}]}}}
% \\
% \smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
% \smallmfield{chart}{$u$.chart}{\textit{Chart}}
% \\
% \smallmfield{e}{$u$.e}{m-interp(chart,move)}}}
% \\
% \smallmfield{commitments}{\smallrecord{\smalltfield{prev}{$r$.commitments}}\d{$\wedge$}$r$.latest-utterance.move.content}{\textit{RecType}}}}}
\newpage
\paragraph{IntegrateOtherAcknowledgement}
(Chapter~\ref{ch:infex})\nopagebreak
$\lambda
r$:\record{\tfield{private}{\record{\tfield{agenda}{$_{\mathit{ne}}$[\textit{RecType}]}}}\\
\tfield{shared}{\record{\tfield{latest-utterance}{
\record{\tfield{move}{
\record{\tfield{content}{\textit{RecType}}}}}}
\\
\tfield{commitments}{\textit{RecType}}}}}
\\
\hspace*{1em}$\lambda
u$:\record{\tfield{move}{fst($r$.private.agenda)\d{$\wedge$}\smallrecord{
\smalltfield{e}{\textit{Acknowledgement}}}\d{$\wedge$}\smallrecord{\smalltfield{e}{\smallrecord{\smallmfield{au}{\textit{SELF}}{\textit{Ind}}}}}
} \\
\tfield{chart}{\textit{Chart}} \\
\tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
\hspace*{2em}\smallrecord{\smalltfield{private}{\smallrecord{\smallmfield{agenda}{rst($r$.private.agenda)}{[\textit{RecType}]}}}
\\
\smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
\smallmfield{chart}{$u$.chart}{\textit{Chart}}
\\
\smallmfield{e}{$u$.e}{m-interp(chart,move)}}}
\\
\smallmfield{commitments}{\smallrecord{\smalltfield{prev}{$r$.commitments}}\d{$\wedge$}$u$.move.cnt}{\textit{RecType}}}}}
% $\lambda
% r$:\record{\tfield{shared}{\record{\tfield{latest-utterance}{
% \record{\tfield{move}{
% \record{\tfield{content}{\textit{RecType}}}}}}
% \\
% \tfield{commitments}{\textit{RecType}}}}}
% \\
% \hspace*{2em}$\lambda
% u$:\record{\tfield{move}{\smallrecord{\smalltfield{e}{\textit{Acknowledgment}} \\
% \smalltfield{c$_{\mathrm{SELF}}$}{addressed(e,SELF)}
% \\
% \smalltfield{cnt}{\textit{RecType}}
% \\
% \smalltfield{c$_{\mathrm{cnt}}$}{content(e,cnt)}}
% } \\
% \tfield{chart}{\textit{Chart}} \\
% \tfield{e}{m-interp(chart,move)}}\hspace*{.5em}. \\
% \hspace*{4em}\smallrecord{
% \smalltfield{shared}{\smallrecord{\smalltfield{latest-utterance}{\smallrecord{\smallmfield{move}{$u$.move}{\textit{Move}} \\
% \smallmfield{chart}{$u$.chart}{\textit{Chart}}
% \\
% \smallmfield{e}{$u$.e}{m-interp(chart,move)}}}
% \\
% \smallmfield{commitments}{\smallrecord{\smalltfield{prev}{$r$.commitments}}\d{$\wedge$}$r$.latest-utterance.move.content}{\textit{RecType}}}}}
\paragraph{Licensing conditions on accommodation updates}
(Chapter~\ref{ch:propnames})\nopagebreak
If $A$ is an agent, $s_i$ is $A$'s current information state, $f$ is a
parametric content of type $T_f$ such that
\begin{quote}
$T_f$ $\sqsubseteq$ \record{\tfield{bg}{\textit{RecType}}\\
\tfield{fg}{(bg$\rightarrow$\textit{RecType})}}
\end{quote}
and
$s_i:_A T_i$ for some $T_i$ such that
\begin{quote}
$T_i$ $\sqsubseteq$ \smallrecord{\smalltfield{ltm}{\textit{RecType}}\\
\smalltfield{gb}{\smallrecord{\smalltfield{shared}{\smallrecord{\smalltfield{commitments}{\textit{RecType}}\\
\smalltfield{latest-move}{\smallrecord{\smallmfield{cont}{$f$}{$T_f$}}}}}}}}
\end{quote}
then \\
\begin{quote}
if there is some $\eta$ which is a relabelling of $f$.bg such that
\begin{quote}
\mbox{$s_i$.gb.shared.commitments $\sqsubseteq$ $[f.\mathrm{bg}]_\eta$}
\end{quote}
% and there is some $\eta'$ which is a labelling of $\mathcal{F}(f)$ such that $\eta'$ is an extension of
% $\eta$,\\[.25\baselineskip]
then $s_{i+1} :_A
T_i$\fbox{\d{$\wedge$}}\textbf{AccGB}($\eta$)($s_i$)($f$) is
licensed\nopagebreak\\[\baselineskip]
else if there is some $\eta$ which is a relabelling of
$f$.bg such that $s_i$.ltm
$\sqsubseteq$ $[f.\mathrm{bg}]_\eta$\nopagebreak\\[.25\baselineskip]
then $s_{i+1} :_A
T_i$\fbox{\d{$\wedge$}}\textbf{AccLTM}($\eta$)($s_i$)($f$) is
licensed\nopagebreak\\[\baselineskip]
else $s_{i+1} :_A
T_i$\fbox{\d{$\wedge$}}\textbf{AccNM}($s_i$)($f$) is
licensed
\end{quote}
\paragraph{\textbf{AccLTM}($\eta$)} (``accommodate match with long
term memory'', Chapter~\ref{ch:propnames})\nopagebreak
$\lambda r$:\record{\tfield{ltm}{\textit{RecType}}\\
\tfield{gb}{(ltm$\rightarrow$\textit{GameBoard})}}\\
\hspace*{1em}$\lambda
f$: \record{\tfield{bg}{\textit{RecType}}\\
\tfield{fg}{(bg$\rightarrow$\textit{RecType})}} . \\
\hspace*{2em} \smallrecord{\smallmfield{ltm}{$r$.ltm}{\textit{RecType}}\\
\smallmfield{gb}{$\lambda r_1$:ltm
. (($r$.gb)($r_1$)\fbox{\d{$\wedge$}}\\\hspace*{3em}\smallrecord{\smalltfield{shared}{\smallrecord{\smallmfield{commitments}{
\smallrecord{\smalltfield{prev}{($r$.gb)($\Uparrow^3$ltm).shared.commitments}\\
\smalltfield{bg}{$f$.bg $\parallel_\eta r_1$}\\
\smalltfield{e}{$f$.fg(bg)}
}}{\textit{RecType}}}}})\\\hspace*{25em}}{(ltm$\rightarrow$\textit{GameBoard})}}
\paragraph{\textbf{AccNM}} (``accommodate no match'',
Chapter~\ref{ch:propnames})\nopagebreak
$\lambda r$:\record{\tfield{ltm}{\textit{RecType}}\\
\tfield{gb}{(ltm$\rightarrow$\textit{GameBoard})}}\\
\hspace*{1em}$\lambda
f$: \record{\tfield{bg}{\textit{RecType}}\\
\tfield{fg}{(bg$\rightarrow$\textit{RecType})}} . \\
\hspace*{2em} \smallrecord{\smallmfield{ltm}{$r$.ltm}{\textit{RecType}}\\
\smallmfield{gb}{$\lambda r_1$:ltm
. (($r$.gb)($r_1$)\fbox{\d{$\wedge$}}\\\hspace*{3em}\smallrecord{\smalltfield{shared}{\smallrecord{\smallmfield{commitments}{
\smallrecord{\smalltfield{prev}{($r$.gb)($\Uparrow^3$ltm).shared.commitments}\\
\smalltfield{bg}{$f$.bg}\\
\smalltfield{e}{$f$.fg(bg)}
}}{\textit{RecType}}}}})\\\hspace*{25em}}{(ltm$\rightarrow$\textit{GameBoard})}}
% $\lambda r$:\record{\tfield{ltm}{\textit{RecType}}\\
% \tfield{gb}{(ltm$\rightarrow$\textit{GameBoard})}}\\
% \hspace*{1em}$\lambda
% f$:$\displaystyle{\bigvee_{T\sqsubseteq [\mathrm{x}:\mathit{Ind}]}}(T\rightarrow \mathit{RecType})$ . \\
% \hspace*{2em} \smallrecord{\smallmfield{ltm}{$r$.ltm}{\textit{RecType}}\\
% \smallmfield{gb}{$\lambda r_1$:ltm
% . (($r$.gb)($r_1$)\fbox{\d{$\wedge$}}\\\hspace*{5em}\smallrecord{\smalltfield{shared}{\smallrecord{\smallmfield{commitments}{\smallrecord{\smalltfield{prev}{($r$.gb)($\Uparrow^3$ltm).shared.commitments}}\d{$\wedge$}$\mathcal{B}(f)$}{\textit{RecType}}}}})\\\hspace*{25em}}{(ltm$\rightarrow$\textit{GameBoard})}}
\paragraph{\textbf{AccGB}($\eta$)}
(``accommodate match on gameboard'',
Chapter~\ref{ch:propnames})\nopagebreak
\textbf{AccGB}($\eta$) =\\
$\lambda r$:\record{\tfield{ltm}{\textit{RecType}}\\
\tfield{gb}{(ltm$\rightarrow$\textit{GameBoard})}} . \\
\hspace*{1em} $\lambda
f$:\smallrecord{\smalltfield{bg}{\textit{RecType}}\\
\smalltfield{fg}{(bg$\rightarrow$\textit{RecType})}}
. \\
\hspace*{2em} \smallrecord{\smallmfield{ltm}{$r$.ltm}{\textit{RecType}}\\
\smallmfield{gb}{$\lambda r_1$:ltm
. $r$.gb($r_1$)\fbox{\d{$\wedge$}}
\smallrecord{\smalltfield{shared}{\smallrecord{\smallmfield{commitments}{\smallrecord{\smalltfield{prev}{$r$.gb.shared.commitments}\\
\smalltfield{bg}{$f$.bg
$\parallel_\eta$
prev}\\
\smalltfield{fg}{$f$.fg(bg)}}}{\textit{RecType}}}}}}{\\\hspace*{30em}(ltm$\rightarrow$\textit{RecType})}}
\section{English resources}
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