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<Paper uid="W03-1013">
  <Title>Log-Linear Models for Wide-Coverage CCG Parsing</Title>
  <Section position="3" start_page="0" end_page="2" type="intro">
    <SectionTitle>
2 The Grammar
</SectionTitle>
    <Paragraph position="0"> Following Clark et al. (2002), we augment CCG lexical categories with head and dependency information. For example, the extended category for persuade is as follows:  The feature [dcl] indicates a declarative sentence; the resulting S[dcl] is headed by persuade; and the numbers indicate dependency relations. The variable X denotes a head, identifying the head of the infinitival complement's subject with the head of the object, thus capturing the object control relation. For example, in Microsoft persuades IBM to buy Lotus, IBM fills the subject slot of buy.</Paragraph>
    <Paragraph position="1"> Formally, a dependency is defined as a 5-tuple:</Paragraph>
    <Paragraph position="3"> is the head word of the functor, f is the functor category (extended with head and dependency information), s is the argument slot, and h a is the head word of the argument. The l is an additional field used to encode whether the dependency is long-range. For example, the dependency encoding Lotus as the object of bought (as in IBM bought Lotus) is represented as follows:</Paragraph>
    <Paragraph position="5"> where is the category (NPnNP)=(S[dcl]=NP) assigned to the relative pronoun. A dependency structure is simply a set of these dependencies.</Paragraph>
    <Paragraph position="6"> Every argument in every lexical category is encoded as a dependency. Unlike Clark et al., we do not require dependencies to be always marked on atomic categories. For example, the marked up category for about (as in about 5,000 pounds)is:</Paragraph>
    <Paragraph position="8"> argument in (4) allows the dependency between about and 5,000 to be captured.</Paragraph>
    <Paragraph position="9"> Clark et al. (2002) give examples showing how heads can fill dependency slots during a derivation, and how long-range dependencies can be recovered through unification of co-indexed head variables.</Paragraph>
  </Section>
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