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<Paper uid="P88-1005">
  <Title>QUANTIFIER SCOPING IN THE SRI CORE LANGUAGE ENGINE</Title>
  <Section position="3" start_page="0" end_page="33" type="intro">
    <SectionTitle>
INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> One of the major sources of ambiguity in sentences results from the different scopes that can be assigned to the various quantified noun phrases in the sentence. Part of the problem in determining the preferred scopings of quantifiers is the number of factors involved. For example, consider these three sentences John visited every house on a street. (1) John visited every house on a square. (2) John visited every patient in a private room. (3) Each of these sentences has two quantifier scopings: in one, &amp;quot;every' has wider scope over &amp;quot;a,&amp;quot; and while in the other, &amp;quot;a&amp;quot; has the wider scope. However, the readings that most people obtain for these sentences are quite different. In (1), the reading in which &amp;quot;a&amp;quot; has wider scope is highly preferred; in (3), the reading in which &amp;quot;everf has wider scope is highly preferred; in (2), the reading with wide-scope &amp;quot;everf is preferred, but wide-scope &amp;quot;a&amp;quot; is also acceptable. A plausible explanation for the difference between (1) and (2) is that, since the typical house is located on a street but not on a square, the default preference represented by (2) is overridden by a conversational maxim of quantity--if &amp;quot;~ streeff has narrow scope, &amp;quot;on a street&amp;quot; would contribute too little information to justify its presence. A plausible explanation for the difference between (2) and (3) is based on the relationship among the components. The reading of (3) in which &amp;quot;a&amp;quot; is given wider scope is improbable because the domain of quantification for &amp;quot;every&amp;quot; would then be the single patient in the selected room--an infelicitous use of &amp;quot;every, ~ whereas there is no similar problem in (2) because there are normally multiple houses on a square.</Paragraph>
    <Paragraph position="1"> Similarly, in John visited a person on every committee. (4) John visited a house on every street. (5) the reading in which &amp;quot;a&amp;quot; has wider scope is reasonable for (4) but not for (5)--in a normal domain of discourse, it is conceivable that there could be a person who is on all of the committees, but it is highly improbable that the geometry of the streets is such that a single house could be located on all of them.</Paragraph>
    <Paragraph position="2"> In (1), (3), and (5), discourse criteria and domain information seem to be the primary factors in determining the preferred quantifier scopings, whereas in (2) and (4), linguistic criteria seem to  be the determining factors.</Paragraph>
    <Paragraph position="3"> Our approach presumes that the determination of a sentence's preferred scoping can be divided into two phases, the first of which is the subject of the algorithm described here. In this initial phase, linguistic information is used to generate the possible quantifier scopings in order of preference. The relevant linguistic information consists of surface position, syntactic structure, and the relationship among the function words (determiners, modals, and negation). In the second phase (future work), domain and discourse information is applied successively to these scopings, modifying the scores produced by the first phase. We expect that the modifications will be only penalties, thus making it possible to identify the best choice when it is encountered (cutting off the processing of remaining scopings generated by the first phase).</Paragraph>
    <Paragraph position="4"> The primary study of quantifier scoping preferences was done by VanLehn (1978). The experimental data reported therein was of limited usefulhess in developing the algorithm described here-it was gathered and evaluated under assumptions arising from a different linguistic theory.</Paragraph>
    <Paragraph position="5"> We shall first present the rules that governed the structure of our design, then outline the algorithm.</Paragraph>
    <Paragraph position="6"> This scoping algorithm has been implemented as a component of a larger system that is under continuing development. In this system, called the Core Language Engine or CLE (Alshawi et aL, 1987), the semantic interpretation phase produces unscoped logical forms in which quantifier expressions are represented by quantifier terms (qterms). For example, the sentence &amp;quot;John saw a studenf' has the uuscoped logical form 1 see'(john';qterm(a',X,student'(X))) Since the only permissible scope for this quantifier is the whole sentence, the qterm is raised to produce the scoped logical form quant(3,X,student'(X), see'(john',X)) The qterm expression can best be thought of as a quant expression before its scope has been established. In the above qterm and quant expressions, student'(X) is the restriction of the quantified variable X; that is, it specifies a set of the possible values of X over which the quantifier ranges. I The logical form's syntax in the implementation is actuaJly \[seel~ohnl,qterm(al,X,\[studentl,X\])\], but the more conventional notation will he ~ for perspicuity.</Paragraph>
    <Paragraph position="7"> In the above quant expression, see'(john',X) is referred to as either the body or the scope of the quantifier. This treatment of the logical form of quantifiers follows that employed in many previous systems (e.g., LUNAR (Woods, 1977), Moore (1981), Barwise and Cooper (1981), and Hobbs and Shieber (1987)).</Paragraph>
  </Section>
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