Towards a Cognitively Plausible Model for Quantification

Towards a Cognitively Plausible Model for Quantification Walid S. Saba AT&T Bell Laboratories 480 Red Hill Rd., Middletown, NJ 07748 USA and Carelton University, School of Computer Science Ottawa, Ontario, KIS-5B6 CANADA walid@eagle.hr.att.com Abstract The purpose of this paper is to suggest that quantifiers in natural languages do not have a fixed truth functional meaning as has long been held in logical semantics. Instead we suggest that quantifiers can best be modeled as complex inference procedures that are highly dynamic and sensitive to the linguistic context, as well as time and memory constraints 1. 1 Introduction Virtually all computational models of quantification are based one some variation of the theory of generalized quantifiers (Barwise and Perry, 1981), and Montague's (1974) (henceforth, PTQ). Using the tools of intensional logic and possible- worlds semantics, PTQ models were able to cope with certain context-sensitive aspects of natural language by devising interpretation relative to a context, where the context was taken to be an "index" denoting a possible- world and a point in time. In this framework, the intension (meaning) of an expression is taken to be a function from contexts to extensions (denotations). In what later became known as "indexical semantics", Kaplan (1979) suggested adding other coordinates defining a speaker, a listener, a location, etc. As such, an utterance such as "I called you yesterday" expressed a different content whenever the speaker, the listener, or the time of the utterance changed. While model-theoretic semantics were able to cope with certain context-sensitive aspects of natural language, the intensions (meanings) of quantJfiers, however, as well as other functional words, such as sentential connectives, are taken to be constant. That is, such words have the same meaning regardless of the context (Forbes, 1989). In such a framework, all natural language quantifiers have their meaning grounded in terms of two logical operators: V (for all), and q (there exists). Consequently, all natural language quantifiers ! The support and guidance of Dr. Jean-Pierre Corriveau of Carleton University is greatly appreciated. are, indirectly, modeled by two logical connectives: negation and either conjunction or disjunction. In such an oversimplified model, quantifier ambiguity has often been translated to scoping ambiguity, and elaborate models were developed to remedy the problem, by semanticists (Cooper, 1983; Le Pore et al, 1983; Partee, 1984) as well as computational linguists (Harper, 1992; Alshawi, 1990; Pereira, 1990; Moran, 1988). The problem can be illustrated by the following examples: (la) Every student in CS404 received a grade. (lb) Every student in CS404 received a course outline. The syntactic structures of (la) and (lb) are identical, and thus according to Montague's PTQ would have the same translation. Hence, the translation of (lb) would incorrectly state that students in CS404 received different course outlines. Instead, the desired reading is one in which "a" has a wider scope than "every" stating that there is a single course outline for the course CS404, an outline that all students received. Clearly, such resolution depends on general knowledge of the domain: typically students in …

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