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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References found in this work BETA
S. C. Kleene (1938). On Notation for Ordinal Numbers. Journal of Symbolic Logic 3 (4):150-155.
Graham Priest (1990). Boolean Negation and All That. Journal of Philosophical Logic 19 (2):201 - 215.
Graham Priest (1979). Logic of Paradox. Journal of Philosophical Logic 8 (1):219-241.
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