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Stabler proposes an implementation of the Chomskyan Minimalist Program,Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits along linguistic tradition. But the semantic calculus is more easily added ifone uses the Curry-Howard isomorphism. Minimalist Categorial Grammars - MCG,based on an extension of the Lambek calculus, the mixed logic, were introducedto provide a theoretically-motivated syntax-semantics interface, Amblard 07. Inthis article, we give full definitions of MG with algebraic tree descriptionsand of MCG, and take the first steps towards giving a proof of inclusion oftheir generated languages.

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