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\def\GF{\textsf{GF}\xspace}
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\title{A GF/MMT, a Framework for Computational Semantics}
\author{Michael Kohlhase, Dennis M\"uller, Frederik Sch\"afer\\Computer Science, FAU
Erlangen-N\"urnberg\\\url{http://kwarc.info}}
\begin{document}
\maketitle
\begin{abstract}
In this note we present how a combination of \GF and \MMT can be used as a development
framework for natural language semantics.
\end{abstract}
\tableofcontents\newpage
Natural language semantics studies systems that represent and compute the meaning of
natural language utterances. It focuses on models that can predict the truth conditions of
an utterance $u$, i.e. for all possible contexts $C$ of $u$, it can predict whether $C(u)$
is valid. Following the ``\defemph{method of fragments}'' introduced in Montague's seminal
paper ``\emph{The proper Treatment of Quantifiers in ordinary Emnglish}''
(PTQ~\cite{Montague:tptoqi73}) such models usually involve
\begin{compactenum}
\item a \defemph{grammar formalism} $G$ that determines a natural language fragment and
can parse this into syntax trees,
\item a \defemph{formal (logical) system} $L$ consisting of a formal language, a model
theory, and a calculus that specifies derivability,
\item a \defemph{semantics construction} process that transforms syntax frees of $G$ into
terms in $L$, and
\item possibly a \defemph{semantic/pragmatic analysis} process that further specifies the
$L$ with respect to the utterance context.
\end{compactenum}
In the three decades following PTQ a plethora of semantics models have been proposed. In
the past, this has been a largely pen-and-paper endeavor. Even though parts of the models
have been implemented, there is no general-purpose framework\footnote{We do not count
high-level programming languages as frameworks here; for these we have extensive,
integrated develoments of models in Prolog~\cite{BlaBos:rainl05} and
Haskell~\cite{EijUng:csfp10} } that allows the effective experimentation with language
models.
\section{Preliminaries}\label{sec:prelim}
\subsection{The Grammatical Framework}\label{sec:gf}
\GF is the ``Grammatical Framework''~\cite{Ranta:GF04,ranta-2011,GF:on}, which seems
uniquely suited for our purposes. It is modular, and it is based (essentially) on LF,
i.e. uses a dependently typed $\lambda$-calculus under the hood. For our purposes,
\cite{Ranta:tlled11} is a treasure trove of insights.
\ednote{cite~\cite{BerChattsfts17}; this combines \GF and Coq for for the Fracas corpus.}
\subsection{\MMT: The Meta-Meta Framework for Meta-Meta Theories}\label{sec:mmt}
\ednote{MK: talk about LATIN, }