Optimal Unification and Learning Algorithms for Categorial Grammars

In this paper continuing [1], we present a more general approach to restricted optimal unification, introduced and applied to learning algorithms for categorial grammars in [2] and further developed in [7,8,4,5]. We introduce a procedure of finding minimal unifiers with respect to some preordering relation between substitutions and solve a general problem of finding all minimal (in several senses) categorial grammars compatible with a given language sample.