Lambek Calculus Enriched with Additional Connectives

摘要

Certain logically natural extensions of the Lambek calculus, which have analogsof conjunction and disjunction, are studied. The Lambek calculus, which underlies a flexible version of categorical grammar, is a special kind of implicational logic, with its slashes corresponding to logical implication. Viewed from this perspective, it makes sense to add other connectives to it, for example, those corresponding to conjunction and disjunction in more standard logics. Some of the formal properties of this enrichment are investigated, especially with respect to the recognizing power of the resulting extended categorical grammars.