The Pentus theorem for Lambek calculus with simple nonlogical axioms (Q817678)

In the paper a version of the Lambek calculus, \(L(\Gamma),\) is considered. The calculus \(L(\Gamma)\) is an associative Lambek calculus \(L\) in Gentzen-style axiomatization, enriched with a finite set of nonlogical axioms \(\Gamma.\) The main result of the paper is the proof of the weak equivalence of the context-free grammars and grammars based on \(L(\Gamma).\) The proof uses, with some modifications, the method applied by Pentus to prove that Lambek categorial grammars generate the context-free languages.