Abstract
In order to deal with some vague assertions more efficiently, fuzzy modal logics have been discussed by many researchers. This paper introduces the notation of fuzzy assertion based on propositional modal logic. As an extension of the traditional semantics about the modal logics, the fuzzy Kripke semantics are considered and the formal system of the fuzzy reasoning based on propositional modal logic is established and the properties about the satisfiability of the reasoning system are discussed.
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