Talking about Trees and Truth-Conditions

An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of (Marcus et al. 1983) was integrated with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990) in (Vijay-Shanker 1992) and was further developed in the ‘D-Tree Grammars’ (DTG) of (Rambow et al. 1995). We generalize Description Theory by integrating semantic information, that is, we propose to tackle both syntactic and semantic underspecification using descriptions. Our focus will be on underspecification of scope. We use a generalized and completely declarative version of the D-Tree formalism. Although trees in our set-up have surface strings at their leaves and are in fact very close to ordinary surface trees, there is also a strong connection with the Logical Forms (LFs) of (May 1977). We associate logical interpretations with these LFs using a technique of internalising the logical binding mechanism (Muskens 1996). The net result is that we obtain a Description Theory-like grammar in which the descriptions underspecify semantics. Since everything is framed in classical logic it is easily possible to reason with these descriptions.