Semantic Abstraction and Anaphora

This paper describes a way of expressing syntactic rules that ~kssociate semantic formulae with strings, but in a manner thai is independent of the syntactic details of these formulac. In particular we show how the same rules construct predicate argument formulae in the style of Montague grammar[131, rap_ resentations reminiscent of situation semantics(Barwise and Perry 121) and of the event logic of Davidson [5], or representations inspired by the discourse representations proposed by Kamp [191. The idea is that semantic representations are specilied 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 quantilier raising in the three different semantic formalisms