Cyclic Pregroups and Natural Language: a Computational Algebraic Analysis Claudia Casadio and Mehrnoosh Sadrzadeh 1 Faculty of Psychology, Chieti University, IT casadio@unich.it 2 Computing Laboratory, Oxford University, UK mehrs@comlab.ox.ac.uk Abstract. 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 intro- ducing appropriate cyclic rules that will allow the grammar to formally analyze and compute word order and movement phenomena in differ- ent 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 com- puting linguistic information. 1 Introduction In this paper we apply logical cyclic rules to the analysis of word order changes in natural languages. The need of some kind of cyclic operations or transformations was envisaged both by Harris [1966, 1968] and Chomsky [1981, 1986] for the treatment of the linguistic contexts referred to with the term movement. In the paper we present a formal approach to natural language based on two cyclic rules that hold in the systems of Noncommutative and Cyclic Multiplicative Linear Logic (NMLL,CyMLL), developed by Abrusci [1991, 2002] from Yetter [1990]. A critical move of this paper is to embed such cyclic rules into the calculus of Pregroups recently introduced by Lambek [1999, 2001, 2008]. The calculus has been succesfully applied to a variety of natural languages from English and German, to French and Italian, and others [see Casadio and Lambek 2008]. We show that the formal grammar obtained by so extending the pregroup calculus allows one to compute string of words belonging to various kinds of natural languages, deriving grammatical sentences involving different types of word order changes or movements, with particular reference to the way in which unstressed clitic pronouns attach to their verbal heads. Cross-linguistic evidence