Non-Commutative Linear Logic in Linguistics

Abstract

This paper explores the linguistic implications of Non-commutative Linear Logic, with particular reference to its multiplicative fragment MNLL, that exhibits a direct relationship to Lambek's Syntactic Calculus. Such a framework is appealing for linguistic analysis since it allows one to develop a dynamic characterization of the notion of a function, that plays a basic role in the foundations of categorial grammar. The analysis will focus on a variety of constructions involving scope configurations, unbounded dependencies and Wh-clauses. Particular attention is given to the proof nets for MNLL, that are planar graphs in which the communication processes and the flow of information are represented by means of a parallelistic architecture. We will introduce proof nets and sequent derivations associated to each linguistic expression and will show that a direct relationship exists between the types and derivations of the Syntactic Calculus and the corresponding types and derivations in MNLL. Moreover, given the symmetric architecture and the crucial role played by the two negations of Non-commutative Linear Logic in the generation of the logical types, we will show that this system is richer in expressive power and in the capacity of performing left-to-right computations of word strings.