Lambek’s Syntactic Calculus and Noncommutative Variants of Linear Logic: Laws and Proof-Nets

This work is devoted to the relations between Lambek’s Syntactic Calculus (LC) and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: (i) the geometrical representation of the laws of LC by means of proof-nets; (ii) the discovery - due to such a geometrical representation - of some laws of LC not yet considered; (iii) the discussion of possible linguistic uses of these new laws.