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

TL;DR

This paper formalizes Minimalist Grammars and Minimalist Categorial Grammars, providing definitions and exploring their language inclusion, aiming to unify syntactic frameworks with semantic integration.

Contribution

It offers formal definitions for MG and MCG and initiates the proof of language inclusion between these two grammatical frameworks.

Findings

Definitions of MG and MCG provided

First steps towards proving language inclusion

Frameworks facilitate syntax-semantics integration

Abstract

Stabler proposes an implementation of the Chomskyan Minimalist Program, Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars - MCG, based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface, Amblard 07. 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 languages.