%%----*- coding: utf-8 -*-

\section{Introduction/Abstract}

%\comment{On avait dit intro sur les modalités~: d'abord Veltman puis
 % subordination}

Epistemic modality involves contextual dependencies in discourse of at least
two kinds~\citep{roberts89,veltman96}.   We characterize them with the slogans:
\begin{enumerate}
\item [I] Epistemic modal facts are asymmetrically dependent on non modal facts.
\item [II] Some modal facts are dependent on other modal facts.
\end{enumerate}
We show
that they have a natural treatment within a continuation style
semantics. 


The first contextual dependency is on display in \posscitet{veltman96} examples:%
\examples{\label{ex:frank}%
  \example{\label{ex:frank-a}It might be sunny.  But it's not sunny}%
  \example{\label{ex:frank-b}\# It's not sunny.  But it might (for all
    I know) be sunny.}%
}%
For Veltman, there is a subtle but unmistakable difference
between (\ref{ex:frank-a}) and (\ref{ex:frank-b}).  The first,
involves a smooth discourse update, whereas the second does not.  The
non modal facts established in prior discourse constrain the set of
epistemic possibilities: if the discourse context contains a non modal
fact that $p$, it does not felicitously admit of a continuation with
the epistemic possibility that $\neg p$.  The converse, however, does
not hold: if the discourse context contains a modal fact that $p$, it
may admit a felicitous continuation that establishes the non modal
fact that $p$. % In section 3.1, we analyze 
%Veltman's ideas.
  %That
%is to say:

%\begin{itemize}
%\item Let X be a state of worlds that represents the information state of the discourse.  Then:
% $$X[\Diamond \phi] = X \mbox{ iff }  \exists w \in X w \in \| \phi \|$$
%\end{itemize}

The phenomenon known as {\em modal subordination} (MS) exemplifies the second dependency of epistemic modalities.
MS involves anaphoric links between
pronouns and their antecedents across modalities like those in (\ref{ex:wolf-might-it-would}) and (\ref{ex:wolf-might-it-will}) from~\cite{roberts89}.  Standard versions of
dynamic semantics~\cite{kamp81} do not predict these links.  
%If we take the modal in ~\exref{ex:wolf-might} to have
%sentential scope, DRT predicts examples such
%as~\exref{ex:wolf-might} to disallow further reference to the discourse
%referent introduced by \textit{a wolf}, whereas this is not the case as~\exref{ex:it-would} attests.
%However, \exref{ex:it-will} shows it should not in some cases. Those
%cases belong to the more general case of \emph{modal subordination}
%where some parts of the discourse have to be interpreted in some
%possible world rather than in the actual one.  Modal subordination can
%be expressed by different means, in particular using modal auxiliaries
%like \textit{might}, \textit{would}, etc.

%\begin{examples}
%\item \label{ex:wolf-might-it-would} A wolf might enter. It would growl.
%\item \label{ex:wolf-might-it-will} A wolf might enter. \wrong It will growl.
%\item \label{ex:enter-would}  A wolf enters. ?It would growl.
%\end{examples}
\examples{
\example{\label{ex:wolf-might-it-would}A wolf might enter. It would growl.}
\example{\label{ex:wolf-might-it-will}A wolf might enter. \wrong It will growl.}
\example{\label{ex:enter-would}A wolf enters. ?It would growl.}}

Previous accounts of dependencies (I) and (II) have exploited DRT or other
dynamic frameworks~\citep{roberts89,veltman96,frank97,stone97}.
We extend the Montagovian continuation semantics of~\citet{degroote06}, to provide a modular treatment of both MS and V.
We embed dynamic modal
logics within a classical setting, where quantifiers, modal operators and variables
receive their standard interpretation and assignments and discourse referents are not semantic objects in the models, 
as they are in most other analyses.%~\citep{groenendijk-stokhof96,dekker99,brasoeavnu10}.  % and show that particular
%choices about the lexical entries of various terms and a particular precisification of the binder properties of the monad used to model discourse semantics
%enable us to treat a wide range of phenomena and intuitions about them.

