We know from the literature in theoretical linguistics that interrogative constructions in Italian have particular syntactic properties, due to the liberal word order and the rich inflectional system. In this paper we show that the calculus of pregroups represents a flexible and efficient computational device for the analysis and derivation of Italian sentences and questions. In this context the distinction between direct vs. indirect statements and questions is explored.

One way of coping with agreement of features in French is to perform two parallel computations, one in the free pregroup of syntactic types, the other in that of feature types. Technically speaking, this amounts to working in the direct product of two free pregroups.

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non- expanding rules must always proceed non-contracting ones in order (...) the derivation to be minimal. We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications. (shrink)