Cyclic pregroups and natural language: a computational algebraic analysis

The calculus of pregroups is introduced by Lambek [1999] as an algebraic computational system for the grammatical analysis of natural languages. Pregroups are non commutative structures, but the syntax of natural languages shows a diffuse presence of cyclic patterns exhibited in different kinds of word order changes. The need of cyclic operations or transformations was envisaged both by Z. Harris and N. Chomsky, in the framework of generative transformational grammar. In this paper we propose an extension of the calculus of pregroups by introducing appropriate cyclic rules that will allow the grammar to formally analyze and compute word order and movement phenomena in different languages such as Persian, French, Italian, Dutch and Hungarian. This cross-linguistic analysis, although necessarily limited and not at all exhaustive, will allow the reader to grasp the essentials of a pregroup grammar, with particular reference to its straightforward way of computing linguistic information.