Constructive logic with strong negation is a substructural logic. II

Studia Logica 89 (3):401 - 425 (2008)
Abstract
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 NFL ew of the substructural logic FL ew . The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL ew (namely, a certain variety of FL ew -algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFL ew . It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic.
Keywords Constructive logic  strong negation  substructural logic  Nelson algebra   $${\mathcal{FL}_{ew}}$$ -algebra  residuated lattice
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