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<Paper uid="E95-1018">
  <Title>Mixing Modes of Linguistic Description in Categorial Grammar</Title>
  <Section position="3" start_page="0" end_page="127" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Categorial Grammar formalisms consist of logics.</Paragraph>
    <Paragraph position="1"> Syntactic information (e.g. subcategorisation, word order) is encoded in complex formulas or types assigned to lexical items. Syntactic derivation is via deduction over lexical formulas. Alternative systems differ in the logics they use, x which may he classified by their limitations on the use of 'resources' (i.e. assumptions) in deduction, and their consequent sensitivity to the specific structuring of those resources (a comparison which gives rise to the 'substructural hierarchy' of logics). In linguistic terms, such logics can be seen to implement different possible views of the nature of linguistic structure.</Paragraph>
    <Paragraph position="2"> In the past few years, categorial systems have been developed that allow access to the resource behaviour of more than one level of the substructural hierarchy. This amounts to a recognition degThe author also at Department of Psychology, Sheffield University. The research reported here was done largely during a year at IRCS, UPenn, with the support of an IRCS Postdoctoral Fellowship award. I would like to thank Ruth Kempson, Natasha Kurtonins, Michael Moortgat, Glyn Morrill and Yde Venema for valuable discussions of the ideas in this paper.</Paragraph>
    <Paragraph position="3"> 1 For example, associative Lambek calculus (Lambek 1958), non-associative Lambek calculus (Lambek 1961), a permutative variant of associative Lambek calculus known as LP (van Benthem 1983), the 'headed' systems of Moortgat &amp; Morrill (1991).</Paragraph>
    <Paragraph position="4"> that a full account of phenomena within a language may require use of more than one notion of linguistic structure, so that e.g. rigid tree-like structures may be appropriate for one class of phenomena (binding, perhaps), whereas more flexible structures may be appropriate for another (coordination, perhaps). Consideration of cross-linguistic variation strengthens the case for allowing multiple notions of structure.</Paragraph>
    <Paragraph position="5"> One approach to creating systems with mixed resource behaviour employs operators called structural modalities. In such work, a specific resource logic is selected as 'basic' for stating the grammar, thereby setting the default characteristics of resource sensitivity. Then, structural modalities are used to allow controlled access to the resource behaviour of other substructural levels.</Paragraph>
    <Paragraph position="6"> Various problems -- theoretical, computational and practical -- arise for the use of such operators. For example, where they are used extensively, unduly complicated accounts tend to result. Also, the need to have a single 'base logic' presents problems for the development of a truly general cross-linguistic framework.</Paragraph>
    <Paragraph position="7"> More recent work has seen the development of approaches that have coexistence of different sublogics within a single mixed or multimodal system. 2 Moortgat &amp; Oehrle (1993;1994) and Hepple (1993) propose general approaches for combining substructural logics into multimodal systems, where 'movement between levels' (enabled by structural modalities in the earlier work) is freely allowed, provided it accords with what are seen to be 'natural relations' between the levels in terms of the relative informativeness of their descriptions. Although developed separately, these two sources propose formal systems that are in many ways similar, but, interestingly, take precisely opposing views as to what are the 'natural relations' between levels. This difference of opinion has consequences for how the systems may be used as linguistic formalisms (requiring, for ex2Some early examples of muitimodal systems are logics that have coexistence, but without interlinkage, of associative and non-associative Lambek calculus (Oehrle &amp; Zhang 1989; Morrill 1990). Further examples include systems that combine associative Lambek calculus with special connectives for discontinuity (e.g. Morrill &amp; Solias 1993; Hepple 1994).</Paragraph>
    <Paragraph position="8">  ample, 'additional apparatus' for handling word order in the second approach), and more crucially for the kind of linguistic accounts they allow to be formulated.</Paragraph>
    <Paragraph position="9"> In this paper, I will describe the approach taken in Hepple (1993) -- what I call the 'hybrid' approach, discuss the general linguistic model that it tends to foster and provide some linguistic illustration, and discuss possibilities for parsing hybrid systems. I will begin with discussion of substructural hierarchy and structural modalities, as it is the behaviour of systems with structural modalities that inspires the hybrid view of how different levels should be related.</Paragraph>
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