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Constructive Logic with Strong Negation is a Substructural Logic. II

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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.

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Authors and Affiliations

  1. Mathematical Institute, University of Bern, CH-3012, Bern, Switzerland

    M. Spinks

  2. Department of Computer Science, University of New Mexico, Albuquerque, NM, 87131, U.S.A

    R. Veroff

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  1. M. Spinks
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  2. R. Veroff
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Spinks, M., Veroff, R. Constructive Logic with Strong Negation is a Substructural Logic. II. Stud Logica 89, 401–425 (2008). https://doi.org/10.1007/s11225-008-9138-1

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