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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 (Vijay-Shanker 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.

The first part of this chapter sketches how to construct Underspecified Discourse Representation Structures (UDRSs, Reyle, 1993) via glue semantics (Dalrymple et al., 1999b). The UDRSs produced bear a close similarity to the ‘skeleton-modifier’ glue representations described by (1998), and like them can typically be constructed in linear time.