Three-valued Logics in Modal Logic

Studia Logica 101 (5):1061-1072 (2013)
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
Keywords Three-valued logic  Modal logic  Conservative translations  Expressivity
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DOI 10.1007/s11225-012-9420-0
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References found in this work BETA
Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.
On Notation for Ordinal Numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
Boolean Negation and All That.Graham Priest - 1990 - Journal of Philosophical Logic 19 (2):201 - 215.
Conservative Translations.Iml D’Ottaviano & H. A. Feitosa - 2001 - Annals of Pure and Applied Logic 108:205-227.
Yes, Virginia, There Really Are Paraconsistent Logics.Bryson Brown - 1999 - Journal of Philosophical Logic 28 (5):489-500.

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Citations of this work BETA
Foreword: Three-Valued Logics and Their Applications.Pablo Cobreros, Paul Égré, David Ripley & Robert van Rooij - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):1-11.

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