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<Paper uid="P96-1011">
  <Title>Efficient Normal-Form Parsing for Combinatory Categorial Grammar*</Title>
  <Section position="6" start_page="85" end_page="85" type="concl">
    <SectionTitle>
7 Conclusions
</SectionTitle>
    <Paragraph position="0"> The main contribution of this work has been formal: to establish a normal form for parses of &amp;quot;pure&amp;quot; Combinatory Categorial Grammar. Given a sentence, every reading that is available to the grammar has exactly one normal-form parse, no matter how many parses it has in toto.</Paragraph>
    <Paragraph position="1"> A result worth remembering is that, although TAG-equivalent CCG allows free interaction among forward, backward, and crossed composition rules of any degree, two simple constraints serve to eliminate all spurious ambiguity. It turns out that all spurious ambiguity arises from associative &amp;quot;chains&amp;quot; such as A/B B/C C or A/B/C C/D D/E\F/G G/H. (Wittenburg, 1987; Hepple &amp; Morrill, 1989) anticipate this result, at least for some fragments of CCG, but leave the proof to future work.</Paragraph>
    <Paragraph position="2"> These normal-form results for pure CCG lead directly to useful parsers for real, restricted CCG grammars. Two parsing algorithms have been presented for practical use. One algorithm finds only normal forms; this simply and safely eliminates spurious ambiguity under most real CCG grammars.</Paragraph>
    <Paragraph position="3"> The other, more complex algorithm solves the spurious ambiguity problem for any CCG grammar, by using normal forms as an efficient tool for grouping semantically equivalent parses. Both algorithms are safe, complete, and efficient.</Paragraph>
    <Paragraph position="4"> In closing, it should be repeated that the results provided are for the TAG-equivalent Bn (generalized composition) formalism of (Joshi et al., 1991), optionally extended with the S (substitution) rules of (Szabolcsi, 1989). The technique eliminates all spurious ambiguities resulting from the interaction of these rules. Future work should continue by eliminating the spurious ambiguities that arise from grammatical or lexical type-raising.</Paragraph>
  </Section>
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