Minimalist grammars are a class of
formal grammar
A formal grammar is a set of Terminal and nonterminal symbols, symbols and the Production (computer science), production rules for rewriting some of them into every possible string of a formal language over an Alphabet (formal languages), alphabe ...
s that aim to provide a more rigorous, usually proof-theoretic, formalization of Chomskyan
Minimalist program
In linguistics, the minimalist program is a major line of inquiry that has been developing inside generative grammar since the early 1990s, starting with a 1993 paper by Noam Chomsky.
Following Imre Lakatos's distinction, Chomsky presents minima ...
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's extensions of the Lambek Calculus
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
, where
is a set of "categorial" features,
is a set of "functional" features (which come in two flavors, "weak", denoted simply
, and "strong", denoted
), and
is a set of lexical atoms, denoted as pairs
, where
is some phonological/orthographic content, and
is a syntactic type defined recursively as follows:
: all features in
and
are (atomic) types, and
: if
and
are types, so are
,
, and
.
We can now define 6 inference rules:
:
, for all
:
, for all
: