Abstract

Distinguishing and dealing with different negations is a basic in fuzzy knowledge representation and reasoning, fuzzy propositional logic formal system with contradictory negation, opposition negation and medium negation (FLcom) is capable of describing various negative relations in fuzzy knowledge. Based on FLcom, the fuzzy modal propositional logic system with three kinds of negations MKcom, as well as MKcom’s expansion systems MTcom, \(\mathrm{MS}_{4}\) com and \(\mathrm{MS}_{5}\) com are proposed in this paper, the semantics of MKcom is discussed, the soundness and completeness theorems of MKcom are proved.

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