Natural deduction systems for some non-commutative logics
Keywordsconstructive sequential propositional logic (COSPL), full Lambek logic (FL), natural deduction, (strong) normalization
AbstractVarieties 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.
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