Studia Logica 101 (5):1061-1072 (2013)
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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
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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
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
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Citations of this work BETA
Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism.Gerhard Schurz - 2022 - Journal of Philosophical Logic 51 (1):27-55.
Conservative Translations of Four-Valued Logics in Modal Logic.Ekaterina Kubyshkina - 2019 - Synthese 198 (S22):5555-5571.
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.
Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
Truth, Pretense and the Liar Paradox.Bradley Armour-Garb & James A. Woodbridge - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag. pp. 339-354.
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