Categorial Grammar and Discourse

Categorial Grammar and Discourse

Representation Theory*

Reinhard Muskens

Abstract

In this paper it is shown how simple texts that can be parsed in a
Lambek Categorial Grammar can also automatically be provided with
a semantics in the form of a Discourse Representation Structure in the
sense of Kamp [1981]. The assignment of meanings to texts uses the
Curry-Howard-Van Benthem correspondence.

1 Introduction

In Van Benthem [1986] it was observed that the Curry-Howard correspon-
dence between proofs and lambda terms can be used to obtain a very elegant
and principled match between Lambek Categorial Grammar and Montague
Semantics. Each proof in the Lambek calculus is matched with a lambda
term in this approach, and Van Benthem shows how this lambda term can
be interpreted as a recipe for obtaining the meaning of the expression that
corresponds to the conclusion of the Lambek proof from the meanings of its
constituent parts.

Usually the semantics that is obtained in this way is an extensional variant
of the semantics given in Montague [1973] (Hendriks [1993] sketches how the
method can be generalized for the full intensional fragment). However, it
is generally acknowledged nowadays that the empirical coverage of classical
Montague Grammar falls short in some important respects. Research in
semantics in the last fifteen years or so has increasingly been concerned with a
set of puzzles for which Montague’s original system does not seem to provide

*From: Proceedings of COLING 94, Kyoto, Japan, 1994, pp. 508-514.

1

1   2   3   4   >>

More intriguing information