A compositional approach to discourse representation theory

Abstract

In a series of articles and talks I Hans Kamp has developed a theory of natural language interpretation that uses discourse representations. The most interesting applications of the theory are the problem of discourse anaphora to indefinites, donkey sentences and temporal processing. It seems likely that the theory can be successfully applied to a range of furlLher questions in natural language semantics. The theory is difficult to compare with Montague Grammar and related approaches to natural language semantics since the system Kamp presents is not a grammar in the sense of Montague (1970). The notion of a grammar in that article is a mathematically precise interpretation of the compositionality principle. Montague requires the syntax and the semantics of the grammar to be expressed as algebras. The relation between the syntactic and the semantic objects must be given as a honaomorphism from the syntactical algebra to the (polynomial closure of) the semantic algebra. If a logical representation language is used in the formulation of the grammar, the relation between the syntactical objects and their representations, and between the representation and their meanings, must again be expressed as homomorphisms between the relevant algebras. In this way, the composition of both homomorphisms is itself a homomorphism between syntax and semantics. The level of representation has thereby only a secondary status in the theory: it helps to develop the grammar by making it more perspicuous, but one can in principle eliminate it in favor of the homomorphism from syntax to semantics it induces. It is the aim of this paper to provide a version of Kamp's ideas that is a grammar in the sense of Montague. In the first part, discourse representation structures will be analysed as a formal language: i.e., a compositional ~ interpretation will be provided. In the second part a fragment of natural language will be defined with a translation in the representation language given in the first part. The fragment is an extension and revision of the fragment in (Kamp, 1981b). Besides comparison with more conventional approaches, there are other reasons for being interested in a compositional formulation of Kamp's ideas. Compositional treatments are supported by a simple theory of how compound expressions get their meaning: it is a function