Three-valued logics in modal logic

Barteld Kooi*, Allard Tamminga

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)
464 Downloads (Pure)

Abstract

Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their originals. This fact raises the question whether there are three-valued logics for which there is a shorter translation into S5. The answer is affirmative: we present an elegant linear translation of the Logic of Paradox and of Strong Three-valued Logic into S5.

Original languageEnglish
Pages (from-to)1061-1072
Number of pages12
JournalStudia Logica
Volume101
Issue number5
DOIs
Publication statusPublished - Oct-2013

Keywords

  • Three-valued logic
  • Modal logic
  • Conservative translations
  • Expressivity
  • PARACONSISTENT LOGICS
  • COMPLEXITY

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