
Decision Problems for Propositional Nonassociative Linear Logic and Extensions
In our previous work, we proposed the logic obtained from full nonassoc...
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A categorical reduction system for linear logic
We build calculus on the categorical model of linear logic. It enables u...
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FitchStyle Modal Lambda Calculi
Fitchstyle modal deduction, in which modalities are eliminated by openi...
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A Linearlogical Reconstruction of Intuitionistic Modal Logic S4
We propose a "modal linear logic" to reformulate intuitionistic modal lo...
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Nonnormal modalities in variants of Linear Logic
This article presents modal versions of resourceconscious logics. We co...
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Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics
We establish decidability for the infinitely many axiomatic extensions o...
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Normal forms for planar connected string diagrams
In the graphical calculus of planar string diagrams, equality is generat...
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On the Lambek Calculus with an Exchange Modality
In this paper we introduce Commutative/NonCommutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/NonLinear 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/noncommutative formalization of the Lambek calculus. Then both of these logics are connected via a pair of monoidal adjoint functors. An exchange modality is then derivable within the logic using the adjunction between both sides. Thus, the adjoint functors allow one to pull the exchange structural rule from the left side to the right side. We then give a categorical model in terms of a monoidal adjunction, and then a concrete model in terms of dialectica Lambek spaces.
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