Constructive Logic with Strong Negation is a Substructural Logic. II
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- Spinks, M. & Veroff, R. Stud Logica (2008) 89: 401. doi:10.1007/s11225-008-9138-1
The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFLew of the substructural logic FLew. The main result of Part I of this series  shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFLew (namely, a certain variety of FLew-algebras) are term equivalent. In this paper, the term equivalence result of Part I  is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFLew. It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic.