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An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

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Abstract

A simple, bivalent semantics is defined for Łukasiewicz’s 4-valued modal logic Łm4. It is shown that according to this semantics, the essential presupposition underlying Łm4 is the following: A is a theorem iff A is true conforming to both the reductionist (rt) and possibilist (pt) theses defined as follows: rt: the value (in a bivalent sense) of modal formulas is equivalent to the value of their respective argument (that is, ‘ A is necessary’ is true (false) iff A is true (false), etc.); pt: everything is possible. This presupposition highlights and explains all oddities arising in Łm4.

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Acknowledgments

Work supported by research project FFI2011-28494, financed by the Spanish Ministry of Economy and Competitiveness. -G. Robles is supported by Program Ramón y Cajal of the Spanish Ministry of Economy and Competitiveness. -We sincerely thank the referees of the JPL for their comments and suggestions on a previous draft of this paper.

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Authors and Affiliations

  1. Campus Unamuno, Edificio FES, Universidad de Salamanca, 37007, Salamanca, Spain

    José M. Méndez

  2. Departamento de Psicología, Sociología y Filosofía, Universidad de León Campus de Vegazana, s/n, 24071, León, Spain

    Gemma Robles & Francisco Salto

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  1. José M. Méndez
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  2. Gemma Robles
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  3. Francisco Salto
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Correspondence to José M. Méndez.

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Méndez, J.M., Robles, G. & Salto, F. An Interpretation of Łukasiewicz’s 4-Valued Modal Logic. J Philos Logic 45, 73–87 (2016). https://doi.org/10.1007/s10992-015-9362-x

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  • DOI: https://doi.org/10.1007/s10992-015-9362-x

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