A note on undecidability of propositional non-associative linear logics

09/30/2019

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by   Hiromi Tanaka, et al.

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We introduce a non-associative and non-commutative version of propositional intuitionistic linear logic, called propositional non-associative non-commutative intuitionistic linear logic (NACILL for short). We prove that NACILL and any of its extensions by the rules of exchange and/or contraction are undecidable. Furthermore, we introduce two types of classical versions of NACILL, i.e., an involutive version of NACILL and a cyclic and involutive version of NACILL. We show that both of these logics are also undecidable.