Partial and paraconsistent three-valued logics

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On the sidelines of classical logic, many partial and paraconsistent three-valued logics have been developed. Most of them differ in the notion of logical consequence or in the definition of logical connectives. This article aims, firstly, to provide both a model-theoretic and a proof-theoretic unified framework for these logics and, secondly, to apply these general frameworks to several well-known three-valued logics. The proof-theoretic approach to which we give preference is sequent calculus. In this perspective, several results concerning the properties of functional completeness, cut redundancy, and proof-search procedure are shown. We also provide a general proof for the soundness and the completeness of the three sequent calculi discussed.

Original languageEnglish
Pages (from-to)143-171
Number of pages29
JournalLogic and Logical Philosophy
Issue number2
Publication statusPublished - 1 Jun 2016


  • Cut redundancy
  • Four-valued logic
  • Functional completeness
  • Paraconsistent logic
  • Partial logic
  • Proof-search procedure
  • Sequent calculus
  • Three-valued logic


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