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Fuzzy Modal Logics


In the paper we introduce formal calculi which are a generalization of propositional modal logics. These calculi are called fuzzy modal logics. We introduce the concept of a fuzzy Kripke model and consider a semantics of these calculi in the class of fuzzy Kripke models. The main result of the paper is the completeness theorem of a minimal fuzzy modal logic in the class of fuzzy Kripke models.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 201–230, 2003.

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Mironov, A.M. Fuzzy Modal Logics. J Math Sci 128, 3461–3483 (2005).

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  • Modal Logic
  • Kripke Model
  • Completeness Theorem
  • Formal Calculus
  • Propositional Modal Logic