Normal forms and functional completeness for four-valued languages

Research output: Contribution to journalArticlepeer-review


Based on the semantic concepts developed by M. Dunn and N. Belnap,
a four-valued language containing only two logical symbols is proposed. We
show that this language is functionally complete with regard to the given
semantics. Specifically, we prove that every truth-function is expressed by
a formula of the language. To do this, we define two concepts akin to the
disjunctive and conjunctive normal forms. Using these concepts, we establish
that every truth-function for a four-valued semantics can be represented
by a formula in a disjunctive form or in a conjunctive form.
Original languageEnglish
Pages (from-to)579 - 588
Number of pages9
JournalBulletin of the Belgian Mathematical Society Simon Stevin
Issue number4
Publication statusPublished - 2015


  • Four-valued logic
  • Functional completeness
  • Disjunctive normal form
  • Conjunctive normal form


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