Minimalist Grammars and Minimalist Categorial Grammars, definitions toward inclusion of generated languages

Abstract. Stabler proposes an implementation of the Chomskyan Min-imalist Program, [1] with Minimalist Grammars- MG, [2]. This frame-work inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimal-ist Categorial Grammars- MCG, based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface, [3]. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated lan-guages. The Minimalist Program- MP, introduced by Chomsky, [1], unified more than fifty years of linguistic research in a theoretical way. MP postulates that a logical form and a sound could be derived from syntactic relations. Stabler, [2], proposes a framework for this program in a computational perspective with Minimalist Grammars- MG. These grammars inherit a long tradition of genera-tive linguistics. The most interesting contribution of these grammars is certainly that the derivation system is defined with only two rules: merge and move. The word Minimalist is introduced in this perspective of simplicity of the definitions of the framework. If the merge rule seems to be classic for this kind of treatment, the second rule, move, accounts for the main concepts of this theory and makes it possible to modify relations between elements in the derived structure. Even if the phonological calculus is already defined, the logical one is more complex to express. Recently, solutions were explored that exploited Curry’s distinction between tectogrammatical and phenogrammatical levels; for example, Lambda Grammars, [4], Abstract Categorial Grammars, [5], and Convergent Grammars [6]. First steps for a convergence between the Generative Theory and Categorial Grammars are due to S. Epstein, [7]. A full volume of Language and Computation proposes several articles in this perspective, [8], in particular [9], and Cornell’s works on links between Lambek calculus and Transformationa