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


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.


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

Mathematics Subject Classification

Primary 03B53 Secondary 03B50 


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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

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