Linguistic Applications of Non-commutative Logic

In this paper I propose linguistic applications of non-commutative logic (NL) developed by Abrusci and Ruet, which constitutes an extension of commutative and non-commutative (cyclic) linear logic. We apply the commutative connec- tives of NL to refine the description of syntactic categories given in Lambek grammars and we use the structural rules of NL to manage the relationship between commutative and non-commutative contexts. In particular, we con- sider local permutation phenomena and unbounded dependencies in Italian, such as topicalization. Moreover a semantic treatment based on proof nets will be given