Ellipsis and Quantification: A Substitutional Approach

Ellipsis and Quantification: A Substitutional Approach Richard Crouch SRI International, Cambridge Computer Science Research Centre 23 Millers Yard, Mill Lane, Cambridge, CB2 1RQ, UK rcecam, sri. tom Abstract The paper describes a substitutional ap- proach to ellipsis resolution giving compa- rable results to (Dalrymple et al., 1991), but without the need for order-sensitive in- terleaving of quantifier scoping and ellip- sis resolution. It is argued that the order- independence results from viewing seman- tic interpretation as building a description of a semantic composition, instead of the more common view of interpretation as ac- tually performing the composition. 1 Introduction Dalrymple, Shieber and Pereira (1991) (hence- forth, DSP) give an equational treatment of ellip- sis via higher-order unification which, amongst other things, provides an insightful analysis of the interac- tions between ellipsis and quantification. But it suf- fers a number of drawbacks, especially when viewed from a computational perspective. First, the precise order in which quantifiers are scoped and ellipses resolved determines the final in- terpretation of elliptical sentences. It is hard to see how DSP's analysis could be implemented within a system employing a pipelined architecture that, say, separates quantifier scoping out from other reference resolution operations--this would seem to preclude the generation of some legitimate readings. Yet many systems, for good practical reasons, employ this kind of architecture. Second, without additional constraints, DSP slightly overgenerate readings for sentences like (1) 3ohn revised his paper before the teacher did, and so did Bill. Kehler (1993a) has convincingly argued that this problem arises because DSP do not distinguish be- tween merely co-referential and co-indexed (in his terminology, role-linked) expressions. Third, though perhaps less importantly, higher- order unification going beyond second-order match- ing is required for resolving ellipses involving quart- tification. This increases the computational com- plexity of the ellipsis resolution task. This paper presents a treatment of ellipsis which avoids these difficulties, while having essentially the same coverage as DSP. The treatment is easily im- plementable, and forms the basis of the ellipsis res- olution component currently used within the Core Language Engine (Alshawi et al., 1992). Ellipsis interpretations are represented as simple sets of substitutions on semantic representations of the antecedent. The substitutions can be built up in an order-independent way (i.e. before, after or during scoping), and without recourse to higher- order unification. The treatment is similar to the discourse copying analysis of (Kehler, 1993a), and to the substitutional treatment suggested by Kamp within Discourse Representation Theory, described in (Gawron and Peters, 1990). However, we extend the notion of strict and sloppy identity to deal with more than just pronouns. In doing so, we readily deal with phenomena like scope parallelism. While the treatment of ellipsis is hopefully of some value in its own right, a more general con- clusion can be drawn concerning the requirements for a computational theory of semantics. Briefly, the standard view within formal semantics, which DSP inherit, identifies semantic interpretation with composition: interpretation is the process of taking the meanings of various constituents and …

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