Applying Pregroups to Italian Statements and Questions

We know from the literature in theoretical and formal linguistics that interrogative constructions in Italian have particular syntactic properties, due to the liberal word order and the rich inflectional system, and therefore represent an interesting subject of investigation. In this paper we show that the calculus of pregroups, a kind of type logical grammar developed by Casadio in cooperation with the mathematician J. Lambek, represents a flexible and efficient computational device for the analysis and derivation of Italian sentences and questions. In the paper we extend the linguistic applications of pregroups to Italian (see Lambek 1999, Casadio & Lambek 2001, Casadio & Lambek 2002) presenting a formal analysis of a distinctive set of direct vs. indirect statements and interrogatives. A pregroup {G, . , 1, , r, →} is a partially ordered monoid in which each element a has a left adjoint and a right adjoint, where the dot “.” Is the unique operation of multiplication with unit 1, interpreted as linguistic concatenation, and the arrow denotes the partial order. Similarly to categorial grammars, a pregroup grammar for a language, such as Italian, consists in two main steps: (i) assign one or more (basic or compound) types to each word in the dictionary; (ii) check the grammaticality and sentencehood of a string of words by a calculation on the corresponding types, where the only rules involved are contractions and appropriate ordering postulates. In particular, in the paper it is shown that in the analysis of direct and indirect question in Italian, on the analogy with Wh-constructions in English, a special role is played by the equations allowing the cancellation of double opposite adjoints. (Lambek 2004). Keywords: Pregroup, inflection, statement, question, wh-question.