On the Expressiveness of Categorial Grammar
Heinrich Wansing · 1995
One of the major contributions of Kazimierz Ajdukiewicz to the philosophy of language is his fundamental work on logical syntax, i.e. Categorial Grammar, in ‘Die syntaktische Konnexität’ (Ajdukiewicz 1935). The present paper addresses a central development in recent investigations of Categorial Grammar, viz. the introduction of new type forming operations (see e.g. Moortgat 1988, Morrill 1990). If the parsing mechanism of Categorial Grammar is conceived of as a propositional logic, the problem is to motivate and to characterize additional propositional connectives. In what follows, a number of additional operations for the Ajdukiewicz-Lambek Calculus of syntactic types is motivated and positive sequential propositional logic (PSPL), i.e. positive propositional logic without structural rules of inference, is suggested as an extended syntactic calculus. Moreover, a higher-level sequent system together with rule-schemata for introducing connectives into premises and conclusions is presented as a definitional framework for characterizing propositional connectives. The connectives of the extended syntactic calculus PSPL are shown to be functionally complete wrt to this proof-theoretic semantics.