Algebraic structures in categorial grammar

In this paper we discuss different algebraic structures which are natural algebraic frames for categorial grammars. First, absolutely free algebras of functor-argument structures and phrase structures together with power-set algebras of types are used to characterize structure languages of Basic categorial grammars and to provide algorithms for equivalence problems and related questions. Second, unification applied to the above frames is employed to develop learning procedures for basic categorial grammars. Third, residuated algebras are used to model language hierarchies of Lambek categorial grammars. The paper focuses on the author's research in this area with references to related works in logic and linguistics. (C) 1998-Elsevier Science B.V. All rights reserved.