Semantic Abstraction and Anaphora

Semantic Abstraction and Anaphora Mark Johnson Brown University Martin Kay Xerox Pale Alto Research Center and Stanford University Abstract This paper describes a way of expressing syn- tactic rules that ~kssociate semantic formulae with strings, but in a manner thai is inde- pendent of the syntactic details of these for- mulac. In particular we show how the same rules construct predicate argument formulae in the style of Montague grammar[131, rap_ resentations reminiscent of situation seman- tics(Barwise and Perry 121) and of the event logic of Davidson [5], or representations in- spired by the discourse representations pro- posed by Kamp [191. The idea is that seman- tic representations are specilied indirectly us- ing semantic construction operators, which en- force an abstraction barrier between the gram- mar and the semantic representations them- selves. 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 Introduction Grammars specifying the relationship between strings and semantic representations often have details of these representations embedded in them. We show how grammar rules can be wrilten in a form which, by abstracting away from details of tim semantic representation, ac- quires greater modularity and hence theoretical perspicuity and practical robustness. In partic- ular, we believe that the approach helps clarify the relationship between apparently disparate theories of semantic representation. 1. The basis of our proposal is that each grammatical rule should contain, or be paired with, an expres- sion written in terms el' sem~mtic construction operators. Different operations can be associ- ated with these operators and, depending on the set in force at a given time, the effect of interpreting the expression will be to construct a representation in one semantic formalism or another. The set of operators contains me,n- bets corresponding to such notions as compo- sitzon, conjttlwtion, etc. The set is small and in- dependent of the semantic formalism. The op- erations are associated with the operators inde- pendently of the grammar and they determine the form of the semantic representation. We present three different sets of seman- tic constructors here, which we have dubbed the predicate-logic, the sets-of-infons and the discourse-representatio,z constructors. We be- gin by introducing the constructors used in this paper: no claims are made for their general sufficiency. Not all of the constructors are rel- evant to all semantic theories and those not needed for a particular one are given degen- crate delinitions. The simplest kind of con- struction operator is the identity function which maps every input i onto just one output, namely i. The operators are the following: 1 The kind of separmion between the granmar and the details of the semanlic representation proposed here also aplxmrs in the examples of Pcreira and Shiebcr[12] and in I.cxicaI-Functional Grammar (see [6]). Our use of different scls of semantic constructors with a single grammar is IR)VCI, aS fa[ aS We are awarg. …

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