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<Paper uid="E89-1003">
  <Title>EFFICIENT PROCESSING OF FLEXIBLE CATEGORIAL GRAMMAR</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
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ABSTRACT*
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    <Paragraph position="0"> From a processing point of view, however, flexible categorial systems are problematic, since they introduce spurious ambiguity. In this paper, we present a flexible categorial grammar which makes extensive use of the product-operator, first introduced by Lambek (1958). The grammar has the prop-erty that for every reading of a sentence, a strictly left-branching derivation can be given. This leads to the definition of a subset of the grammar, for which the spurious ambiguity problem does not arise and efficient processing is possible.</Paragraph>
    <Paragraph position="1"> 1. Flexibility vs. Ambiguity Categorial Grammars owe much of their popularity to the fact that they allow for various degrees of flexibility with respect to constituent structure. From a processing point of view, however, flexible categorial systems are problematic, since they introduce spurious ambiguity.</Paragraph>
    <Paragraph position="2"> The best known example of a flexible categorial grammar is a grammar containing the reduction rules application and composition, and the category changing rule raising 1 * * I would like to thank Esther K0nig, Erik-Jan van der Linden, Michael Moortgat, Adriaan van Paassen and the participants of the Edinburgh Categorial Grammar Weekend, who made useful comments to earlier presentations of this material. All remaining errors and misconceptions are of course my own.</Paragraph>
    <Paragraph position="3"> 1 Throughout this paper we will be using the notation of Lambek (1958), in which  With this grammar many alternative constituent structures for a sentence can be generated, even where this does not correspond to semantic ambiguities. From a linguistic point of view, this has many advantages. Various kind of arguments for giving up traditional conceptions of constituent structure can be given, but the most convincing and well-documented case in favour of flexible constituent structure is coordination (see Steedman (1985), Dowty (1988), and Zwarts (1986)).</Paragraph>
    <Paragraph position="4"> The standard assumption in generative grammar is that coordination always takes place between between constituents. Right-node raising constructions and other instances of non-constituent conjunction are problematic, because it is not clear what the status of the coordinated elements in these constructions is. Flexible categorial grammar presents an elegant solution for such cases, since, next to canonical constituent structures, it also admits various other constituent structures. Therefore, the sentences in (2) can be considered to be ordinary instances of coordination (of two categories slap and (vp/ap)\vp, respectively).</Paragraph>
    <Paragraph position="5"> (2) a. John sold and Mary bought a book s/vp vp/np s/vp vp/np np s/np s/np left-directional functor respectively, looking for an argument of category B.</Paragraph>
    <Paragraph position="6">  A somewhat different type of argument for flexible phrase structure is based on the way humans process natural language. In Ades &amp; Steedman (1982) it is pointed out that humans process natural language in a left-to-right, incremental, manner. This processing aspect is accounted for in a flexible categorial system, where constituents can be built for any part of a sentence. Since syntactic rules operate in parallel with semantic interpretation rules, building a syntactic structure for an initial part of a sentence, implies that a corresponding semantic structure can also be constructed.</Paragraph>
    <Paragraph position="7"> These and other arguments suggest that there is no such thing as a fixed constituent structure, but that the order in which elements combine with eachother is rather free. From a parsing point of view, however, flexibility appears to be a disadvantage.</Paragraph>
    <Paragraph position="8"> Flexible categorial grammars produce large numbers of, often semantically equivalent, derivations for a given phrase. This spurious ambiguity problem (Wittenburg (1986)) makes efficient processing of flexible categorial grammar problematic, since quite often there is an exponential growth of the number of possible derivations, relative to the length of the string to be parsed.</Paragraph>
    <Paragraph position="9"> There have been two proposals for eliminating spurious ambiguity from the grammar. The first is Wittenburg (1987). In this paper, a categorial grammar with composition and heavily restricted versions of raising (for subject n p's only) is considered. Wittenburg proposes to eliminate spurious ambiguity by redefining composition. His predictive composition rules apply only in those cases where they are really needed to make a derivation possible. A disadvantage of this method, noticed by Wittenburg, is that one may have to add special predictive composition rules for all general combina- 20 tory rules in the grammar. Some careful rewriting of the original grammar has to take place, before things work as desired.</Paragraph>
    <Paragraph position="11"> efficient chart-parsing algorithm for categorial grammars with spurious ambiguity. Instead of the usual strategy, in which all possible subconstituents are added to the chart, Pareschi &amp; Steedman restrict themselves to adding only those constituents that may lead to a difference in semantics. Thus, in (3)  only the underlined constituents are in the chart. The &amp;quot;---&amp;quot; constituent is not. (3) John loves Mary madly s/vp vp/np np vp\vp  Combining 'madly' with the rest would be impossible or lead to backtracking in the normal case. Here, the Pareschi &amp; Steedman algorithm starts looking for a constituent left adjacent of madly, which contains an element X/vp as a leftmost category. If such a constituent can be found, it can be concluded that the rest of that constituent must (implicitly) be a v p, and thus the validity of combining vp\vp with this constituent has been established. Therefore, Pareschi &amp; Steedman are able to work with only a minimal amount of items in the chart.</Paragraph>
    <Paragraph position="12"> Both Wittenburg and Pareschi &amp; Steedman work with categorial grammars, which contain restricted versions of composition and raising. Although they can be processed efficiently, there is linguistic evidence that they are not fully adequate for analysis of such phenomena as coordination. Since atomic categories can in general not be raised in these grammars, sentence (2b) (in which the category n p has to be raised) cannot be derived. Furthermore, since composition is not generalized, as in Ades &amp; Steedman (1982), a sentence such as John sold but Mary donated a book to the library would not be derivable. The possibilities for left-to-right, incremental, processing are also limited. Therefore, there is reason to look for a more flexible system, for which efficient parsing is still possible.</Paragraph>
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