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<Paper uid="P88-1006">
  <Title>A General Computational Treatment of Comparatives for Natural Language Question Answering</Title>
  <Section position="3" start_page="41" end_page="42" type="intro">
    <SectionTitle>
2. Aa Initial Exmnple
</SectionTitle>
    <Paragraph position="0"> The mechanisms we shall describe apply a conventional series of transformations to sentences containing one or more comparatives, ultimately resulting in an executable expression. As an example of this process, 2 we'll consider the input &amp;quot;List the cars at lee.st 20 inches more tlum twice as long as the Century is wide&amp;quot; which contains a highly comparativized adjective.</Paragraph>
    <Paragraph position="1"> First, this input is scanned and parsed, yielding the parse tree shown in Figure 1. Note that each COMPAR node has a QUANTITY node and a MODE 3 of its own. Also, the MODE of the top COMPAR (whose value is &amp;quot;equal') is co-indexed (indicated by the subsrcipt i) with the MODE feature associate with the panicle ('as') that intervenes between the ADJ and its COMPAR-ARG; this assures that -er/than, less/than, and as/as pairs collocate correctly. Next, we build a &amp;quot;normalized&amp;quot; parse tree by reconstructing elements that were discontinuous in the surface structure and  2. A formal account the associated formalisms, including a BNF syntax and a denotational semantics for our &amp;quot;normalized parse trees&amp;quot; and &amp;quot;algebraic-logical form&amp;quot; language, is given in Ballard and Stumberger (1987).</Paragraph>
    <Paragraph position="2"> 3. Dashed lines indicate features, as distinct from lcxical items, and empty nodes, which result from Whiz-deletion, are denoted by'?'.</Paragraph>
    <Paragraph position="3">  by performing other simplifications. This yields the following structure, whose 2-place predicate, with P  (parameter) and A (argument) as variables, corresponds to &amp;quot;at least 20 inches more than twice as * .. as'.</Paragraph>
    <Paragraph position="4">  Next, user-defined meanings of words and phrases are looked up 4 and the comparati~zafion operations described in Section 6 are performed, yielding</Paragraph>
    <Paragraph position="6"> Finally, this representation is converted into the executable expression indicated by</Paragraph>
    <Paragraph position="8"> where KSV and KI are primitive retrieval functions of the Kandor back-end; @I{...}, @F{...} and @S{...} are Lisp objects respectively denoting instances, frames, and slots in Kandor's taxonomic knowledge base; and &gt;I&gt;/ is a coercion routine supplied by TELI to accommodate backend retrieval system that produce numbers in disguise (e.g. a Lisp object or a singleton set) on which the standard Lisp functions would choke. 5 However, since compositionally created structures such as the preceding one are often intolerably inefficient, optimiz~tions are carried out while the executable expression is being formed. In the case at hand, the second argument of &gt;I &gt;~ is constant, so it is evaluated, producing</Paragraph>
    <Paragraph position="10"> A second example, which illustrates a comparative  4. In TELI, meanings may be arbitrary expressions in the extended tint-order language discussed in Ballard and Stumberger (1987).</Paragraph>
    <Paragraph position="11"> 5. Similar functions are also supplied for arithmetic operators.  quantifier, is given in an appendix where, as a result of optimizations analogous to those which produced the constant 158 above, the comparative &amp;quot;at least 3 more large cars than Buick&amp;quot; is eventually processed exactly as though it had been &amp;quot;at least 6 cars&amp;quot; (since Buick made 3 large cars).</Paragraph>
  </Section>
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