Algebraic Structures in Categorial Grammar

Wojciech Buszkowski 
Faculty of Mathematics and Computer Science
Adam Mickiewicz University, 60-769 Pozna\'n, Poland 
E-mail: buszko@math.amu.edu.pl

Abstract

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 powerset 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.

Key words: categorial grammar, type logics, type algebras,
Lambek calculus, residuated semigroup.