Logica Universalis

, Volume 11, Issue 4, pp 507–524 | Cite as

The Pursuit of an Implication for the Logics L3A and L3B

  • Alejandro Hernández-Tello
  • José Arrazola Ramírez
  • Mauricio Osorio Galindo
Article

Abstract

The authors of Beziau and Franceschetto (New directions in paraconsistent logic, vol 152, Springer, New Delhi, 2015) work with logics that have the property of not satisfying any of the formulations of the principle of non contradiction, Béziau and Franceschetto also analyze, among the three-valued logics, which of these logics satisfy this property. They prove that there exist only four of such logics, but only two of them are worthwhile to study. The language of these logics does not consider implication as a connective. However, the enrichment of a language with an implication connective leads us to more interesting systems, therefore we look for one implication for these logics and we study further properties that the logics obtain when this connective is added to these systems.

Keywords

Genuine paraconsistent logic implication Gödel’s implication non-classical logics 

Mathematics Subject Classification

Primary 03B53 Secondary 03B50 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arieli, O., Avron, A., Zamansky, A.: Ideal paraconsistent logics. Stud. Logica 99(1), 31 (2011)MATHMathSciNetGoogle Scholar
  2. 2.
    Baaz, M. et al.: Infinite-valued gödel logics with \(0 \)-\(1 \)-projections and relativizations. In: Gödel’96: Logical Foundations of Mathematics, Computer Science and Physics—Kurt Gödel’s Legacy, Brno, Czech Republic, August 1996, proceedings, pp. 23–33. Association for Symbolic Logic (1996)Google Scholar
  3. 3.
    Béziau, J.-Y.: Are paraconsistent negations negations? Lecture notes in pure and applied mathemathics, pp. 465–486 (2002)Google Scholar
  4. 4.
    Béziau, J.-Y.: What is paraconsistent logic. In: In Batens et al.[6. Citeseer (2000)Google Scholar
  5. 5.
    Beziau, J.Y.: Two genuine 3-valued paraconsistent logics. In: Akama, S. (ed.) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol. 110. Springer, Cham (2016)Google Scholar
  6. 6.
    Beziau, J.Y., Franceschetto, A.: Strong three-valued paraconsistent logics. In: Beziau, J.Y., Chakraborty, M., Dutta, S. (eds.) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol. 152. Springer, New Delhi (2015)Google Scholar
  7. 7.
    Carballido, J.L., Osorio, M., Arrazola, J.R.: Equivalence for the-stable models semantics. J. Appl. Logic 8(1), 82–96 (2010)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Galindo, M.O., Macías, V.B., Ramírez, J.R.E.A.: Revisiting da costa logic. J. Appl. Logic 16, 111–127 (2016)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Gödel, Kurt: Zum intuitionistischen aussagenkalkül. Anz. Akad. Wiss. Wien 69, 65–66 (1932)MATHGoogle Scholar
  10. 10.
    Priest, Graham: Dualising intuitionictic negation. Principia 13(2), 165 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alejandro Hernández-Tello
    • 1
  • José Arrazola Ramírez
    • 1
  • Mauricio Osorio Galindo
    • 2
  1. 1.Facultad de Cs. Físico-MatemáticasBenemérita Universidad Autónoma de PueblaPueblaMexico
  2. 2.Departamento de MatemáticasFundación Universidad de las AméricasPueblaMexico

Personalised recommendations