Advertisement

Journal of Logic, Language and Information

, Volume 17, Issue 1, pp 89–107 | Cite as

The basic constructive logic for a weak sense of consistency

  • Gemma Robles
  • José M. Méndez
Original Article

Abstract

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

Keywords

Constructive negation Substructural logics Ternary relational semantics Paraconsistent Logic 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Méndez J.M., Salto F. (2000) Intuitionistic propositional logic without contraction but with reductio. Studia Logica 66: 409–418CrossRefGoogle Scholar
  2. Méndez J.M., Salto F., Robles G. (2002) Anderson and Belnap’s minimal implicative logic with minimal negation. Reports on Mathematical Logic 36: 117–130Google Scholar
  3. Priest, G., & Tanaka, K. (2004). Paraconsistent logic. In Zalta, E. N. (Ed.), The Standford Encyclopedia of Philosophy. Winter 2004 Edition. URL:http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/.Google Scholar
  4. Robles, G., & Méndez, J. M. (2005, March). On defining constructive negation in logics of entailment. Paper presented at the 1st World Congress on Universal Logic, Montreux, Switzerland.Google Scholar
  5. Robles, G., Méndez, J. M., & Salto, F. (2007). Relevance logics, paradoxes of consistency and the K rule. Logique et Analyse, 50, number 198, to appear in June. (An abstract of this paper was presented at the Logic Colloquium 2006, Nijmegen (The Netherlands), July 27–August 2).Google Scholar
  6. Routley, R., et al. (1982). Relevant logics and their rivals, vol. 1. Atascadero, CA: Ridgeview Publishing Co..Google Scholar
  7. Slaney, J. (1995). MaGIC, matrix generator for implication connectives: Version 2.1, notes and guide. Canberra: Australian National University.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.c Los OsoriosLeónSpain
  2. 2.Universidad de SalamancaSalamancaSpain

Personalised recommendations