Natural deduction systems for some non-commutative logics

Norihiro Kamide, Motohiko Mouri

DOI: http://dx.doi.org/10.12775/LLP.2007.005

Abstract


Varieties of natural deduction systems are introduced for Wansing’s paraconsistent non-commutative substructural logic, called a constructive sequential propositional logic (COSPL), and its fragments. Normalization, strong normalization and Church-Rosser theorems are proved for these systems. These results include some new results on full Lambek logic (FL) and its fragments, because FL is a fragment of COSPL.

Keywords


constructive sequential propositional logic (COSPL); full Lambek logic (FL), natural deduction; (strong) normalization

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