Structural Control

Abstract

If unification has been the champion of “alternative” grammar in the last decade, transformation has been that of “standard” grammar for the last three. Here, as was the case for unification, we find a special analogue of transformation in a certain bearing of categorial logic. Structural modalities, or exponentials as they are known in linear logic, were introduced by Girard (1987) to control manipulations of resources by structural rules in logic. We advocate the same strategy of modal-isation at the lower reaches of the structural hierarchy with which we are concerned for the purposes of grammar. The overall picture is one of primitive structure-changing operations free to apply in any configuration meeting certain conditions on structure and categories. This is reminiscent of the notion of transformation developed in its classical form in e.g. Chomsky’s (1965, p.147) Aspects of the Theory of Syntax:

“…we can apparently define a grammatical transformation in terms of a “structure index” that is a Boolean condition on Analyz-ability and a sequence of elementary transformations drawn from a base set including substitutions, deletions, and adjunctions.”