M. Hepple. 1993. A General Framework for Hybrid Substructural Categorial Logics. (Draft of August 1993.) Available as: IRCS Technical Report 94-14. Institute for Research in Cognitive Science, University of Pennsylvania.

Abstract:

For the class of systems known as Categorial Grammars, grammar formalisms consist of logics. Lexical assignment is of complex formulas or types, which by their structure may encode various syntactic information. Syntactic derivation is via deduction over lexical formulas. Alternative categorial systems differ in the logic they employ to provide a notion of derivability.

There exist a wide range of different logics, which may be classified with respect to their limitations (if any) on the use of the resources that are available to serve deduction, and their consequent sensitivity to the specific structured nature of those resources. Comparison of logics in these terms gives rise to the so-called `substructural hierarchy of logics'. Various systems on this hierarchy have been employed within Categorial Grammar. It has become clear, however, that access to more than one substructural level is required not only cross-linguistically, for producing the grammars of very different languages, but also for specifying the grammar of any one language. The most plausible current model for how this may be done involves firstly selecting a specific resource logic as the `basic' logic. This choice sets the default characteristics of resource sensitivity. Then, special modal operators, termed structural modalities, may be used to allow controlled access to the resource sensitivity of higher substructural levels. A number of theoretical, computational and practical problems arise for the use of such operators. In this paper, I propose an alternative general model of hybrid substructural systems, which should eliminate the need for structural modalities. The new model exploits natural relations between different substructural levels in terms of the relative informativeness of their characterisations. Under this model, the range of substructural levels form a single unified descriptive system, which may be used for different languages, although very different languages will tend to exploit different modes of description made available by the overall system. Such a unified approach should both facilitate producing grammars for individual languages, and provide a better basis for cross-linguistic generalisation.