The Normal and Self-extensional Extension of Dunn–Belnap Logic

Arnon Avron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A logic L is called self-extensional if it allows to replace occurrences of a formula by occurrences of an L-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, the famous Dunn–Belnap four-valued logic has (up to the choice of the primitive connectives) exactly one self-extensional four-valued extension which has an implication. We also investigate the main properties of this logic, determine the expressive power of its language (in the four-valued context), and provide a cut-free Gentzen-type proof system for it.

Original languageEnglish
Pages (from-to)281-296
Number of pages16
JournalLogica Universalis
Issue number3
StatePublished - 1 Sep 2020


FundersFunder number
Israel Science Foundation817/15


    • Four-valued logics
    • Paraconsistent logics
    • Self-extensionality


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