Mixing Modes of Linguistic Description in Categorial Grammar

Mixing Modes of Linguistic Description in Categorial Grammar Mark Hepple Department of Computer Science, University of Sheffield, Regents Court, Portobello Street, Sheffield S1 4DP, UK Email: hepple@dcs, sheffield, ac. uk Abstract Recent work within the field of Categorial Grammar has seen the development of ap- proaches that allow different modes of lo- gical behaviour to be displayed within a single system, something corresponding to making available differing modes of lin- guistic description. Earlier attempts to achieve this goal have employed modal op- erators called structural modalities, whose use presents a number of problems. I pro-. pose an alternative approach, involving co- existence and interrelation of different sub- logics, that eliminates the need for struc- tural modalities, whilst maintaining the de- scriptive power they provide. 1 Introduction Categorial Grammar formalisms consist of logics. Syntactic information (e.g. subcategorisation, word order) is encoded in complex formulas or types assigned to lexical items. Syntactic deriv- ation is via deduction over lexical formulas. Al- ternative systems differ in the logics they use, x which may he classified by their limitations on the use of 'resources' (i.e. assumptions) in deduc- tion, and their consequent sensitivity to the spe- cific 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. In the past few years, categorial systems have been developed that allow access to the resource behaviour of more than one level of the substruc- tural hierarchy. This amounts to a recognition °The 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 Kurton- ins, Michael Moortgat, Glyn Morrill and Yde Venema for valuable discussions of the ideas in this paper. 1 For example, associative Lambek calculus (Lam- bek 1958), non-associative Lambek calculus (Lam- bek 1961), a permutative variant of associative Lam- bek calculus known as LP (van Benthem 1983), the 'headed' systems of Moortgat & Morrill (1991). that a full account of phenomena within a lan- guage 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 allow- ing multiple notions of structure. One approach to creating systems with mixed resource behaviour employs operators called structural modalities. In such work, a specific re- source logic is selected as 'basic' for stating the grammar, thereby setting the default characterist- ics of resource sensitivity. Then, structural mod- alities are used to allow controlled access to the resource behaviour of other substructural levels. Various problems -- theoretical, computational and practical -- arise for the use of such oper- ators. For example, where they are used extens- ively, unduly complicated …

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