Predicate logic unplugged

Abstract

this paper we describe the syntax and semantics of a description language for underspecified semantic representations. This concept is discussed in general and in particular applied to Predicate Logic and Discourse Representation Theory. The reason for exploring underspecified representations as suitable semantic representations for natural language expressions emerges directly from practical natural language processing applications. The so-called Combinatorial Explosion Puzzle, a well known problem in this area, can succesfully be tackled by using underspecified representations. The source of this problem, scopal ambiguities in natural language expressions, is discussed in section 2. The core of the paper presents Hole Semantics. This is a general proposal for a framework, in principle suitable for any logic, where underspecified representations play a central role. There is a clear separation between the object language (the logical language one is interested in) and the meta language (the language that describes and interprets underspecified structures). It has been noted by various authors that the meaning of an underspecified semantic representation cannot be expressed in terms of a disjunction of denotations, but rather as a set of denotations (cf. Poesio 1994). We support this view, and use it as underlying principle for the definition of the semantic interpretation function of underspecified structures. Section 3 is an informal introduction to Hole Semantics, and in section 4 things are formally defined. In section 5 we apply Hole Semantics to Predicate Logic, resulting in an "unplugged" version of (static and dynamic) Predicate Logic. In section 6 we show that this idea easily carries over to Discourse Representation Structures. A lot of attention has been paid..