Studia Logica

, Volume 88, Issue 3, pp 325–348

Constructive Logic with Strong Negation is a Substructural Logic. I


DOI: 10.1007/s11225-008-9113-x

Cite this article as:
Spinks, M. & Veroff, R. Stud Logica (2008) 88: 325. doi:10.1007/s11225-008-9113-x


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 [30]. 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 [40] 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.


Constructive logicstrong negationsubstructural logicNelson algebraFLew-algebraresiduated lattice

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of EducationUniversity of CagliariCagliariItaly
  2. 2.Department of Computer ScienceUniversity of New MexicoAlbuquerqueU.S.A.