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Journal of Philosophical Logic

, Volume 45, Issue 1, pp 73–87 | Cite as

An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

  • José M. Méndez
  • Gemma Robles
  • Francisco Salto
Article

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.

Keywords

Many-valued logics Modal logics 4-valued logics Łukasiewicz’s 4-valued modal logic Bivalent semantics 

Notes

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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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • José M. Méndez
    • 1
  • Gemma Robles
    • 2
  • Francisco Salto
    • 2
  1. 1.Campus Unamuno, Edificio FESUniversidad de SalamancaSalamancaSpain
  2. 2.Departamento de Psicología, Sociología y FilosofíaUniversidad de León Campus de Vegazana, s/nLeónSpain

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