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Constructive Logic with Strong Negation is a Substructural Logic. II

Spinks, M. ; Veroff, R.

In: Studia Logica, 2008, vol. 89, no. 3, p. 401-425

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    Titre
    • Constructive Logic with Strong Negation is a Substructural Logic. II
    Auteur
    • Spinks, M.. Mathematical Institute, University of Bern, CH-3012, Bern, Switzerland
    • Veroff, R.. Department of Computer Science, University of New Mexico, 87131, Albuquerque, NM, U.S.A
    Type de document
    • Postprint
    Identifiant OAI-PMH
    • oai:doc.rero.ch:322006
    Summary
    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