Extending Lambek Grammars to Basic Categorial Grammars

Pentus [24] proves the equivalence of LCG’s and CFG’s, and CFG’s are equivalent to BCG’s by the Gaifman theorem [1]. This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen [12], but it was deficient [4]. We use a modification of Pentus’ proof and a new proof of the Gaifman theorem on the basis of the Lambek calculus.