Constructive Logic with Strong Negation is a Substructural Logic. I
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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. In this paper, it is shown 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. This answers a longstanding question of Nelson . Extensive use is made of the automated theorem-prover Prover9 in order to establish the result.
The main result of this paper is exploited in Part II of this series  to show that the deductive systems N and NFLew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FLew.
KeywordsConstructive logic strong negation substructural logic Nelson algebra FLew-algebra residuated lattice
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