Computer Science ›› 2017, Vol. 44 ›› Issue (4): 263-268.doi: 10.11896/j.issn.1002-137X.2017.04.055

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Fuzzy Modal Propositional Logic with Three Kinds of Negation

CHEN Cheng, PAN Zheng-hua and LV Yong-xi   

  • Online:2018-11-13 Published:2018-11-13

Abstract: In the fuzzy knowledge processing,it is a basic theory for distinguishing,expressing,reasoning and calculating for different negative knowledge.The fuzzy propositional logic formal system FLCOM with contradictory negation,opposition negation and medium negation is a theory which can fully describe the different negation with its relation and law in fuzzy knowledge.In this paper,a fuzzy modal propositional logic system MKCOM with three kinds of negation was proposed based on FLCOM and the medium modal propositional logic MK,as well as the expansion system MTCOM,MS4COM and MS5COM of MKCOM.Then the interpretation of semantics and syntax about MKCOM was discussed,and the reliability and completeness theorems of MKCOM were proved.

Key words: Fuzzy propositional logic formal system,Medium modal propositional logic,Fuzzy modal propositional logic

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