On the computation of joins for non associative Lambek categorial grammars

This paper deals with an application of unification and rewriting to Lambek categorial grammars used in the field of computational linguistics. Unification plays a crucial role in the acquisition of categorial grammar acquisition, as in [Kan98] ; a modified unification has been proposed [For01a] in this context for Lambek categorial grammars, to give an account of their logical part. This modified unification ( ‖= unification) relies both on deduction (Lambek derivation) and on substitution ; it is strongly related to the conjoinability relation [Lam58,Pen93] that is characterized by a free group equivalence and by a quasi-group one in the non-associative version. In view of grammatical inference, we also need to compute joins of the conjoinability relation, when they exists. This paper deals with this issue for the non-associative version of Lambek grammars, and provides an algorithm based on quasi-group rewriting.