An interpretation of łukasiewicz’s 4-valued modal logic

• Autores: José Manuel Méndez Rodríguez, Gemma Robles Vázquez, Francisco Salto Alemany
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 45, Nº. 1, 2016, págs. 73-87
• Idioma: inglés
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• Resumen

  • 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.