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}
}
  • Jiaming Jiang, Harley D. Eades, Valeria de Paiva
  • Published in Linearity-TLLA@FLoC 2018
  • Mathematics, Computer Science
  • CoRR
  • 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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