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<Paper uid="P91-1010">
  <Title>TYPE-RAISING AND DIRECTIONALITY IN COMBINATORY GRAMMAR*</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
PRELIMINARIES
</SectionTitle>
    <Paragraph position="0"> In Categorial Grammar (CG), elements like verbs are associated with a syntactic &amp;quot;category&amp;quot;, which identifies their functional type. I shall use a notation in which the argument or domain category always appears to the right of the slash, and the result or range category to the left. A forward slash / means that the argument in question must appear on the right, while a backward slash \ means it must appear on the left.</Paragraph>
    <Paragraph position="2"> The category (S\NP)/NP can be regarded as both a syntactic and a semantic object, in which symbols like S are abbreviations for graphs or terms including interpretations, as in the unification-based categorial grammars ofZeevat et al. \[8\] and others (and cf. \[6\]). Such functions can combine with arguments of the appropriate type and position by rules of functional application, written as follows:  (2) The Functional Application Rules: a. X/Y Y =~ X (&gt;) b. Y X\Y :=~ X (&lt;)  Such rules are also both syntactic and semantic rules *Thanks to Michael Niv and Sm Shieber. Support from: NSF Grant CISE IIP CDA 88-22719, DARPA grant no. N0014-90J1863, and ARO grant no. DAAL03-89-C0031. of combination in which X and Y are abbreviations for more complex objects which combine via unification. They allow context-free derivations like the following (the application of rules is indicated by in- null The derivation can be assumed to build a compositional interpretation, (enjoy' musicals') mary', say. Coordination can be included in CG via the following rule, allowing constituents of like type to conjoin to yield a single constituent of the same type:  (4) X conj X =~ X (5) I love and admire musicals  ................................</Paragraph>
    <Paragraph position="3"> ........................</Paragraph>
    <Paragraph position="4"> (s\m')/m, The rest of the derivation is exactly as in (3). In order to allow coordination of contiguous strings that do not constitute constituents, CCG allows certain operations on functions related to Curry's combinatots \[1\]. Functions may compose, as well as apply, under rules like the following:</Paragraph>
  </Section>
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