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<Paper uid="P95-1051">
  <Title>Towards a Cognitively Plausible Model for Quantification</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> 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).</Paragraph>
    <Paragraph position="1"> 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 &amp;quot;index&amp;quot; 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).</Paragraph>
    <Paragraph position="2"> In what later became known as &amp;quot;indexical semantics&amp;quot;, Kaplan (1979) suggested adding other coordinates defining a speaker, a listener, a location, etc. As such, an utterance such as &amp;quot;I called you yesterday&amp;quot; expressed a different content whenever the speaker, the listener, or the time of the utterance changed.</Paragraph>
    <Paragraph position="3"> 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.</Paragraph>
    <Paragraph position="4"> 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.</Paragraph>
    <Paragraph position="5"> (lb) Every student in CS404 received a course outline.</Paragraph>
    <Paragraph position="6"> 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 &amp;quot;a&amp;quot; has a wider scope than &amp;quot;every&amp;quot; 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 the same class receive the same course outline, but different grades. Due to the compositionality requirement, PTQ models can not cope with such inferences. Consequently a number of syntactically motivated rules that suggest an ad hoc semantic ordering between functional words are typically suggested. See, for example, (Moran, 1988) 2 .</Paragraph>
    <Paragraph position="7"> What we suggest, instead, is that quantifiers in natural language be treated as ambiguous words whose meaning is dependent on the linguistic context, as well as time and memory constraints.</Paragraph>
  </Section>
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