# On the Lambek Calculus with an Exchange Modality

@article{Jiang2018OnTL, title={On the Lambek Calculus with an Exchange Modality}, author={Jiaming Jiang and Harley D. Eades and Valeria de Paiva}, journal={CoRR}, year={2018}, volume={abs/1904.06847}, pages={43-89} }

In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should view this logic as composed of two logics; one sitting to the left of the other. On the left, there is intuitionistic linear logic, and on the right is a mixed commutative/non-commutative formalization of the Lambek calculus. Then both of these logics are… CONTINUE READING

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