Semantic Abstraction and Anaphora

This paper describes a way of expressing syntactic rules that associate semantic formulae with strings, but in a manner that is independent of the syntactic details of these formulae. In particular we show how the same rules construct predicate argument formulae in the style of Montague grammar[13], representations reminiscent of situation semantics(Barwise and Perry [2]) and of the event logic of Davidson [5], or representations inspired by the discourse representations proposed by Kamp [9]. The idea is that semantic representations are specified indirectly using semantic construction operators, which enforce an abstraction barrier between the grammar and the semantic representations themselves. First we present a simple grammar which is compatible with the three different sets of constructors for the three formalisms. We then extend the grammar to provide one treatment that accounts for quantifier raising in the three different semantic formalisms