Description theory, LTAGs and underspecified semantics

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) has been integrated in (VijayShanker 1992) with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). 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 version of ltag, to which we shall refer as lftag. Although trees in lftag 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.