Studia Logica

, 89:401 | Cite as

Constructive Logic with Strong Negation is a Substructural Logic. II

Article

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 NFLew of the substructural logic FLew. 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 NFLew (namely, a certain variety of FLew-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 NFLew. 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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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of BernBernSwitzerland
  2. 2.Department of Computer ScienceUniversity of New MexicoAlbuquerqueU.S.A

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