Lambek Calculus for Transformational Grammar

In this paper we present a formalization of some ideas from Chomsky (1995) in the framework of multimodal type logical grammar (e.g., Moortgat (1996) and refs). This project is in many respects rather straightforward, but makes use of aspects of the type logical machinery which are generally not used, or at least not used for these purposes, in categorial grammar. This allows us to investigate to some degree the relation between analyses of extraction phenomena based on hypothetical reasoning—the classical categorial approach—and those based on movement, seen here as a complex of structural rules fed by product types appearing in lexical type formulas.