Decision Problems for Propositional Non-associative Linear Logic and Extensions

03/03/2020

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by   Hiromi Tanaka, et al.

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In our previous work, we proposed the logic obtained from full non-associative Lambek calculus by adding a sort of linear-logical modality. We call this logic non-associative non-commutative intuitionistic linear logic (NACILL, for short). In this paper, we establish the decidability and undecidability results for various extensions of NACILL. Regarding the decidability results, we show that the deducibility problems for several extensions of NACILL with the rule of left-weakening are decidable. Regarding the undecidability results, we show that the provability problems for all the extensions of non-associative non-commutative classical linear logic by the rules of contraction and exchange are undecidable.