Two Accounts of Scope Availability and Semantic Underspecification

Two Accounts of Scope Availability and Semantic Underspecification Alistair Willis and Suresh Manandhar, Department of Computer Science, University of York, York Y010 5DD, UK. {agw, suresh}@cs, york. ac. uk Abstract We propose a formal system for representing the available readings of sentences displaying quan- tifier scope ambiguity, in which partial scopes may be expressed. We show that using a theory of scope availability based upon the function- argument structure of a sentence allows a deter- ministic, polynomial time test for the availabil- ity of a reading, while solving the same problem within theories based on the well-formedness of sentences in the meaning language has been shown to be NP-hard. 1 Introduction The phenomenon of quantifier scope ambigu- ity has been discussed extensively within com- putational and theoretical linguistics. Given a sentence displaying quantifier scope ambiguity, such as Every man loves a woman, part of the problem of representing the sentence's meaning is to distinguish between the two possible mean- ings: Vx(ma (x) -+ 3y(woma (y) A lo e(x, y))) where every man loves a (possibly) different woman, or where a single woman is loved by every man. One aspect of the problem is the generation of all available readings in a suitable representa- tion language. Cooper (1983) described a sys- tem of "storing" the quantifiers as A-expressions during the parsing process and retrieving them at the sentence level; different orders of quan- tifier retrieval generate different readings of the sentence. However, Cooper's method generates logical forms in which variables are not correctly bound by their quantifiers, and so do not cor- respond to a correct sentence meaning. This problem is rectified by nested storage (Keller, 1986) and the Hobbs and Shieber (1987) al- gorithm. However, the linguistic assumptions underlying these approaches have recently been questioned. Park (1995) has argued that the availability of readings is determined not by the well-formedness of sentences in the meaning lan- guage, but by the function-argument relation- ships within the sentence. His theory proposes that only a subset of the well-formed sentences generated by nested storage are available to a speaker of English. Although the theories have different generative power, it is difficult to find linguistic data that convincingly proves either theory correct. In the absence of persuasive linguistic data, it is reasonable to ask whether other grounds exist for choosing to work with either of the two theories. This paper considers the appli- cation of both theories to the problem of un- derspecified meaning representation, and the question of determining whether a set of con- straints represents an available reading of an ambiguous sentence or not. We show that a constraint language based upon Park's linguis- tic theory (Willis and Manandhar, 1999) solves this problem in polynomial time, and contrast this with recent work based on dominance con- straints which shows that using the more per- missive theory of availability to solve the same problems leads to NP-hardness. 2 Underspecification A recent area of interest has been with under- specified representations of an ambiguous …

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