Minimalist grammar

Minimalist grammars are a class of formal grammars that aim to provide a more rigorous, usually proof-theoretic, formalization of Chomskyan Minimalist program than is normally provided in the mainstream Minimalist literature. A variety of particular formalizations exist, most of them developed by Edward Stabler, Alain Lecomte, Christian Retoré, or combinations thereof.

Lecomte and Retoré (2001) introduce a formalism that modifies that core of the Lambek Calculus to allow for movement-like processes to be described without resort to the combinatorics of Combinatory categorial grammar. The formalism is presented in proof-theoretic terms. Differing only slightly in notation from Lecomte and Retoré (2001), we can define a minimalist grammar as a 3-tuple ${\displaystyle G=(C,F,L)}$, where ${\displaystyle C}$ is a set of "categorial" features, ${\displaystyle F}$ is a set of "functional" features (which come in two flavors, "weak", denoted simply ${\displaystyle f}$, and "strong", denoted ${\displaystyle f*}$), and ${\displaystyle L}$ is a set of lexical atoms, denoted as pairs ${\displaystyle w:t}$, where ${\displaystyle w}$ is some phonological/orthographic content, and ${\displaystyle t}$ is a syntactic type defined recursively as follows:

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