Self-extensional three-valued paraconsistent logics have no implication

Arnon Avron*, Jean Yves Beziau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A proof is presented showing that there is no paraconsistent logics with a standard implication (or even semi-implication) which have a three-valued characteristic matrix, and in which the replacement principle holds.

Original languageEnglish
Pages (from-to)183-194
Number of pages12
JournalLogic Journal of the IGPL
Issue number2
StatePublished - 1 Apr 2017


  • Implication
  • Many-valued logic
  • Negation
  • Paraconsistent logic
  • Self-extensionality


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