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<Paper uid="E89-1003">
  <Title>EFFICIENT PROCESSING OF FLEXIBLE CATEGORIAL GRAMMAR</Title>
  <Section position="8" start_page="0" end_page="0" type="concl">
    <SectionTitle>
6. Coordination
</SectionTitle>
    <Paragraph position="0"> The P-calculus is structurally complete, and therefore, all the arguments that have been presented in favour of a categorial analysis of coordination, hold for the P-calculus as well. Coordination introduces polymorphism in the grammar, however, and this leads to some complications for the restricted P-calculus presented in (12).</Paragraph>
    <Paragraph position="1"> Adding a category X\(X/X) for coordinators to the P-calculus, enables us to handle non-constituent conjunction, as is exemplified in (17) and (18).</Paragraph>
    <Paragraph position="2">  The restricted-calculus of (12) was designed to enable efficient left-associative parsing. We assumed that lexieal categories would always be product-free, but this assumption no longer holds, if we add X\(X/X) to the grammar (since X can be instantiated, for instance as s/vp*vp/np). This means that left-associative derivations are not always possible for coordinated sentences.</Paragraph>
    <Paragraph position="3"> Our solution to this problem, is to add rules such as (19) to the grammar, which can transform certain product-categories into product-free categories.</Paragraph>
    <Paragraph position="4"> (19) A/(B*C) ~&gt; (A/C)/B A number of such rules are needed to restore left-associativity.</Paragraph>
    <Paragraph position="5"> Next to syntactical additions, some modifications to the semantic part of the inference rule P had to be made, in order to cope with the polymorphic semantics proposed for coordination by Partee &amp; Rooth (1983).</Paragraph>
    <Paragraph position="6"> 7. Concluding remarks.</Paragraph>
    <Paragraph position="7"> The spurious ambiguity problem has been solved in this paper in a rather paradoxical manner. Whereas Wittenburg (1987) tries to do away with ambiguous phrase structure as much as possible (it only arises where you need it) and Pareschi &amp; Steedman (1987) use a chart parsing technique to recover implicit constituents efficiently, the strategy in this paper has been to go for complete ambiguity. It is in fact this massive ambiguity, which trivializes constituent structure to such an extent that one might as well ignore it, and choose a constituent structure that fits ones purposes best (left-branching in this case). It seems that as far as processing is concerned, the half-way flexible systems of Steedman (having generalized composition, and heavily restricted forms of raising) are in fact the hardest case. Simple AB-grammars are in all respects similar to CF-grammars, and can directly be parsed by any bottom-up algorithm. For strong structurally complete systems such as P, spurious ambiguity can be eliminated by inspecting left-branching trees only. For flexible but not structurally complete systems, it is much harder to predict which derivations are interesting and which ones are not, and therefore the only solution is often to inspect all possibilities. - 25 -</Paragraph>
  </Section>
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