Categorial Grammar and Discourse Representation Theory

CATEGORIAL GRAMMAR AND DISCOURSE REPRESENTATION THEORY Reinhard Muskens Institute for Language Technology and Artificial Intelligence (ITK) PO Box 90153, 5000 LE, Tilburg, The Netherlands, R.A.Muskens@kub.nl 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. O. INTRODUCTION In Van Benthem [1986] it was observed that the Curry-Howard correspondence between proofs and lamtxla terms can be used to obtain a very el- egant and principled match between Lambek Categorial Grammar and Montague Semantics. Each proof in the gambek calculus is matched with a lambda term in this approach, and Van Benthem shows how this lambda term can be in- terpreted 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 fi'agment). However, it is gen- erally 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 in- creasingly been concerned with a set of puzzles for which Montague's original system does not seem to provide us with adequate answers. The puzzles I am referring to have to do with the intri- cacies of anaphoric linking. What is the mecha- nism behind ordinary cross-sentential anaphora, as in 'Harry has a cat. He feeds it'? Is it essen- tially the same mechanism as the one that is at work in the case of temporal anaphora? I low is it possible that in Geach's notorious 'donkey' sentences, such as 'If a farmer owns a donkey, he beats it', the noun phrase 'a farmer' is linked to the anaphoric pronoun 'it' without its having scope over the conditional and why is it that the noun phrase is interpreted as a universal quanti- tier, not as an existential one? While it has turned out rather fi'uitless to stt, dy these and similar questions within classical Mon- tague Grammar (MG), they can be studied prof- itably within the framework of Discourse Representation Theory (DRT, see Heim [1982, 1983], Kamp [1981], Kamp & Reyle [1993]). This semantic theory offers interesting analyses of tile phenomena that were mentioned above and many researchers in the field now adopt some form of DRT as the formalism underlying their semantical investigations. But the shift of paradigm seems to have its drawbacks too. Barwise [1987] and Rooth [198711, for example, observe that the new theory does not give us the nice unified account of norm phrases as generalized quantifiers that Monta- gut's approach had to offer and it is also clear from Ka,n 1) & …

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