Studia Logica 101 (5):1061-1072 (2013)

Authors
Allard Tamminga
University of Greifswald
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

Modal Logic: An Introduction.Brian F. Chellas - 1980 - Cambridge University Press.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Logic for Equivocators.David Lewis - 1982 - Noûs 16 (3):431-441.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
On Notation for Ordinal Numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.

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Citations of this work BETA

Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
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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