Conjoinability and unification in Lambek categorial grammars
Annie Foret · 2001
Recently, learning algorithms in Gold’s model have been proposed for some particular classes of classical categorial grammars [Kan98]. We are interested here in learning Lambek categorial grammars. In general grammatical inference uses unification and substitution. In the context of Lambek categorial grammars it seems appropriate to incorporate an operation on types based both on deduction (Lambek derivation) and on substitution instead of standard substitution and standard unification. After an introduction (in connection with learning), this paper will re-call conjoinability results [Lam58, Pen93]- using groups-; we then con-sider a characterization of conjoinability- using quasi-groups- for the non-associative version of Lambek calculus. We then relate these characteriza-tions to the modified unification investigated in [For01] for the associative Lambek calculus. 1