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<Paper uid="P04-1014">
  <Title>Parsing the WSJ using CCG and Log-Linear Models</Title>
  <Section position="3" start_page="0" end_page="0" type="intro">
    <SectionTitle>
2 Parsing Models for CCG
</SectionTitle>
    <Paragraph position="0"> CCG is unusual among grammar formalisms in that, for each derived structure for a sentence, there can be many derivations leading to that structure. The presence of such ambiguity, sometimes referred to as spurious ambiguity, enables CCG to produce elegant analyses of coordination and extraction phenomena (Steedman, 2000). However, the introduction of extra derivations increases the complexity of the modelling and parsing problem.</Paragraph>
    <Paragraph position="1"> Clark et al. (2002) handle the additional derivations by modelling the derived structure, in their case dependency structures. They use a conditional model, based on Collins (1996), which, as the authors acknowledge, has a number of theoretical deficiencies; thus the results of Clark et al. provide a useful baseline for the new models presented here.</Paragraph>
    <Paragraph position="2"> Hockenmaier (2003a) uses a model which favours only one of the derivations leading to a derived structure, namely the normal-form derivation (Eisner, 1996). In this paper we compare the normal-form approach with a dependency model.</Paragraph>
    <Paragraph position="3"> For the dependency model, we define the probability of a dependency structure as follows:</Paragraph>
    <Paragraph position="5"> where is a dependency structure, S is a sentence and ( ) is the set of derivations which lead to .</Paragraph>
    <Paragraph position="6"> This extends the approach of Clark et al. (2002) who modelled the dependency structures directly, not using any information from the derivations. In contrast to the dependency model, the normal-form model simply defines a distribution over normal-form derivations.</Paragraph>
    <Paragraph position="7"> The dependency structures considered in this paper are described in detail in Clark et al. (2002) and Clark and Curran (2003). Each argument slot in a CCG lexical category represents a dependency relation, and a dependency is defined as a 5-tuple hh f; f; s;ha;li, where h f is the head word of the lexical category, f is the lexical category, s is the argument slot, ha is the head word of the argument, and l indicates whether the dependency is long-range.</Paragraph>
    <Paragraph position="8"> For example, the long-range dependency encoding company as the extracted object of bought (as in the company that IBM bought) is represented as the following 5-tuple: hbought;(S[dcl]nNP1)=NP2;2;company; i where is the category (NPnNP)=(S[dcl]=NP) assigned to the relative pronoun. For local dependencies l is assigned a null value. A dependency structure is a multiset of these dependencies.</Paragraph>
  </Section>
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