Journal of Philosophical Logic

, Volume 45, Issue 1, pp 73–87

# An Interpretation of Łukasiewicz’s 4-Valued Modal Logic

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

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## Authors and Affiliations

• José M. Méndez
• 1
Email author
• 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