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\section{Attitude dynamics}


Modal subordination also occurs between pairs of attitude reports involving one or more cognitive agents. Consider:
\examples{%
\example{\label{want}Sam wants to marry an Italian.  He hopes she will be rich.}
\example{\label{hob-nob}Hob thinks a witch has blighted his mare, and Nob thinks she has given his cow warts.}}
CS is flexible enough to allow lexical entries inducing a wide scope reading for the existential quantifier over unembedded modalities for MS.  The intuitive truth conditions for (\ref{want}) and (\ref{hob-nob}) require such modal independence. In (\ref{want}) Sam doesn't \emph{want} to hope that
his Italian is rich---he simply hopes that she will be rich.  Similarly, (\ref{hob-nob}) is not intuitively a report about what Hob believes about Nob or vice-versa.  
%In (\ref{want}), Sam has a certain desire, to marry an Italian.   This could be a {\em de dicto} desire, in that he has no particular Italian in mind.  Furthermore, he hopes that the Italian that he marries will be rich.  We can handle this within the modal framework by adopting a particular lexical entries in which the hope is conditionally dependent upon the object of desire's realization.  That is, the hope modality picks up the modal continuation provided the desire modality.%\footnote{Though much simpler and more elegant than the DRT strategies, this adaptation of continuation style semantics follows the strategy proposed in Asher 1987 in DRT and Heim 1990, though Asher also countenances more complex strategies for the Hob Nob example.}  
  
%This strategy does not suffice for (\ref{hob-nob}), however.  For   
The wide-scope strategy yields the following for (\ref{hob-nob}), given an empty left context and trivial continuation:
%This example poses a problem for standard first order belief representations, as it is impossible to capture its intuitive truth conditions with ordinary scope bearing quantifiers and operators, unless we make substantive assumptions about the domains of our intensional models.  For instance, (\ref{hob-nob1}) provides a first order representation of (\ref{hob-nob}); but  
\example{\label{hob-nob1}$\exists x \ (\believes_{h} (\semof{witch}(x) \wedge  \semof{blighted ...}(x)) \wedge \believes_{n} (\semof{gave warts...}(\sel \ ((x::\nil)))))$}
The truth of (\ref{hob-nob1}) problematically requires that there is an object in the world of evaluation that is a witch in all of Hob and Nob's belief worlds.  The witch could be entirely a figment of Hob and Nob's imagination.  We don't want the truth conditions of such reports to rest on substantive assumptions about the metaphysics of modality.

\citep{asher87} provided the first dynamic treatment of such examples.  He exploited the contents of DRSs as sets of world assignment pairs (as \citeauthor{frank97} would do later for modal subordination), and coordinated the interpretations of two attitude descriptions by constraining the proper embeddings of each to agree on assignments to certain pairs of discourse referents.  %These constraints extend the notion of {\em internal} anchors introduced in~\citep{asher86}.  
On such an approach, {\em a witch} in (\ref{hob-nob} was treated introducing material only within the scope of the belief operator;%\footnote{Contra \cite{kamp-forthcoming} who believes that such internal anchors must also have external anchors.} 
various possible witches could be the value of this variable or discourse referent under the coordinated assignments.  The Hob-Nob examples, like the MS examples, showed the peculiarities of the logical framework of DRT in which discourse referents have a kind of hybrid status, somewhere between bound and free variables. 
%More concretely, suppose Hob and Nob believe there are three witches in Hob and Nob's home town Witchville.  It could be that two of these that have been recently active and either or perhaps both would satisfy the coordinated beliefs of Hob and Nob.

% When giving a first order translation of a DRS for an extensional ``first order'' fragment of English, we tend to treat the discourse referents in the top DRS as existentially bound variables.  But once we move to an intensional fragment, there is pressure to treat top level discourse referents in those DRSs that characterize attitudes or modal claims as free variables.  

To capture \posscitet{asher87}'s interpretation of (\ref{hob-nob} but the curious logical status of the discourse referents in DRT, we propose that the truth conditions of (\ref{hob-nob}) entail
Hob and Nob's sharing of an individual concept.  Without going into details (though see~\citep{asher10}), the story exploits coercion and our $\TEST$ operator of section 3.  The pronoun in the second sentence presupposes the presence of an antecedent of the appropriate type.  Like other presuppositional triggers, the pronoun places a $\TEST$ on the antecedent context that there be an antecedent of the appropriate type in the left context.  Given our interpretive assumptions, this is not the case.  Thus, the $\TEST$ fails.  But the semantics of the pronoun also licenses an accommodation mechanism for the exception, whereupon the antecedent changes its type from $\ent$ to $s \rightarrow \ent$, the type of an individual concept.\footnote{We can imagine the same sort of test mechanism to be triggered not only because the context fails the $\TEST$ for semantic reasons, as here, but also for pragmatic reasons, as in the famous paycheck sentences--- {\em the man who gave his paycheck to his wife was wiser than the one who gave it to his mistress}.}   To treat the exception, we then redo the entire computation having lifted the type of the indefinite to a quantifier over individual concepts.  

To treat the exception case for the $\TEST$ properly, we must precisify the particular kind of individual concept at issue.  The intuitive truth conditions of (\ref{hob-nob}) dictate that we need to ensure that the extension of the concept in Nob's belief worlds and the
extension of the concept in Hob's worlds are such that: if witch A  blighted Hob's mare in  a Hob belief world, then at least some of the belief worlds of Nob will have witch A giving his cow warts; and all of Nob's belief worlds, anyone who gave Nob's cow warts is a witch who blighted Hob's mare in one of Hob's belief worlds.  This is what the coordinated dependencies of~\cite{asher87} captures. This will require a more complex binder rule  making special use of the modal continuation.
%After the pronoun selects for the intensional element in the factual left context, we get this:%
%\begin{equation}
%\label{hn-lf}
%{\small
%\exists x^{\small s \rightarrow e} (\believes_h (\semof{witch}(x) \wedge \semof{blighted-horse}(^{\vee}x, u)))  \believes_n \  \semof{gave-warts}(^{\vee}x, u))))}
%\end{equation}
%This is close to what is desired.  But %this way of treating the exception to the $\TEST$ on the context by the interpretation of the pronoun 
%it doesn't ensure coreference at the objectual level.  And it is objectual coreference that is intuitively required.  The variable in (\ref{hn-lf}) must over concepts that have same instantiations across the belief worlds of Hob and Nob, and \emph{furthermore} the belief worlds of Nob are dependent upon the choice of value for the individual concept.   %There is a dependency of Nob's belief worlds on the values of the individual concept in Nob's world.  %The type of the individual concept required for dealing with this report is quite complex: it is a function from two or more sets of worlds ( the belief sets of our agents) into
%an individual concept. 

TY2, with an added basic type for worlds, proves useful for treating the exception to the $\TEST$.  In the language of TY2, roughly all predicates that were n-ary become n+1 ary with the addition of a world parameter.   The exception rule forces the evaluation of the concept in Nob's belief worlds to be the same  the extension of the concept in some one of Hob's belief worlds.  The end result is this:
\example{\label{hn-lf'} $\lambda w \exists x^{\small s \rightarrow e} ( \forall w' \in \believes_{h,w}(\semof{witch}(x(w'), w') \wedge \semof{\semof{blighted-horse}}(x(w'), w') \ \wedge  \exists w_1 \in \believes_{n,w} x(w_1) = x(w') \ \wedge \forall w'' \in \believes_{n,w} (\semof{gave-warts}(x(w''), w'') \wedge \exists w''' \in \believes_{h,w} x(w''') = x(w''))))$}
Thus, CS proves very useful in the analysis of dependencies between modalities and between modal and factual information.  
%
%Our analysis of the anaphoric dependency in (\ref{hob-nob}) is not completely satisfactory, because Nob's beliefs seem a little too dependent on the evaluation of the witch concept in Hob's belief worlds.  The truth conditions for (\ref{hn-lf'}) are such that every object that satisfies Hob's reported beliefs in one of his belief worlds must satisfy Nob's reported beliefs in {\em all} of his belief worlds.  This seems too strong, no longer have an existential force here but in effect a universal one.  How could we remedy this situation?  The exception rule would have to avail itself of the fact that there are two modal continuations that must be harmonized together.   This requires a more sophisticated view of what counts as a left context; the context has to be at the very least a sequence of left contexts in our sense here.  We would then have to have recourse to a new kind of context dependency, a back and forth dependency, which we must encode within a special %kind of individual concept--- a {\em dependent} individual concept relative to two modal continuations.
%\examples{$x$ is a d-concept (dc) relative to two modal continuations iff,\\
% $\forall w' \in \believes_{a, w} \ \exists w'' \in \believes_{b, w} \ x(w') = x(w'')$ and $\forall w'' \in \believes_{b, w}  \ \exists w' \in \believes_{a, w} \  x(w'') = x(w')$}
%Using dc's allows finally to give the right truth conditions for (\ref{hob-nob}).
%\example{\label{hn-lf''} $\lambda w \exists x^{\small \mbox{\sc dc}}  \forall w' \in \believes_{h,w}(((\semof{witch}(x(w'), w') \wedge \exists ! u (\semof{h's mare}(u, w') \wedge \semof{blighted}(x(w'), u), w')) \ \wedge \forall w'' \in \believes_{n,w \rangle} (\exists ! v (\semof{h's cow}(v,w'') $ \\
%\hspace*{.4in} $\wedge \ \semof{killed}(x(w''), u,w'')))$}
%This gives us the right binding properties for the individual concept.\footnote{We can define {\sc dic}s in intensional logic as well, we believe, though the use of TY2 has a heuristic
%value.
%}
%, as long as we have a left context in which the
%independence of two modal contexts can be recorded.  We would then have:\\
%A concept $c_A$ is a {\sc dic} relative to modal contexts $A$ and $B$ just in case $\forall w' \in B_w \exists w'' \in A \ c_B(w') = c_A(w'') \wedge \forall w'' \in A \exists w' \in B_w  \ c_B(w') = c_A(w'') $\\

%By rewriting the exception rule using {\sc dic}s, we will get the right sort of coordinated beliefs as truth conditions for Hob Nob sentences.  We can then treat such examples without resorting to TY2.}
%\begin{examples}
%\example{\label{hn-lf''} $ \exists x^{\mbox{\sc dic}} B_h(((\semof{witch}(\downarrow x) \wedge \exists ! u (h's \semof{mare}(u) \wedge \semof{blighted}(\downarrow x, u))) \ \wedge B_{h, \langle   \rangle} (\exists ! v (h's \semof{cow}(v,') $ \\
%\hspace*{.4in} $\wedge \ \semof{killed}(\downarrow x, u)))$}

