Deductive and grammatical competence: Type logical remarks on nesting phenomena

The aim of this work is to present some applications of a theory of grammatical competence to the problem of the deductive competence of cognitive agents. The point of view here adopted is from the theory of categorial grammars and the research program from them developed, namely the so called logical approach to grammar. This research program remarkably extended the range of linguistic phenomena that can be described by means of logical notions, applying tools from linear logic. Without entering the technical details, we present briefly the essential features of this research program, focusing on the aspects that are important for the proposed application, mainly focusing on the logical nature of this kind of formalism. After describing and limiting the kind of deductive competence we can deal with, I will make some considerations about a theory of deductive competence intended as a logical calculus, and I will present some application of a theory which can represent the grammatical competence to the problem of describing the deductive competence. At the end, I will propose an example which suggests a comparison between the notion of complexity involved in the deductive and grammatical competence.