Sound and Complete Axiomatic System with a Modality □φ=1V2φ
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    Abstract:

    This paper proposes a propositional modal logic with a modality □φ=1V2φ, and specifies the language, the syntax and the semantics for the logic. The axiomatic system for is sound and complete, where 1 and 2 are given in this paper. The axiomatic system for the logic has the similar language, but has the different syntax and semantics. For any formula φ, □φ=1V2φ; the frame for the axiomatic system is defined as an tripleW,R1,R2, and the model is defined as quadruple W,R1,R2,I. When the completeness theorem is proved, two equivalence relations are constructed on the set that is made up of all the maximal consistent sets. The construction method of a canonical model for the axiomatic system is different from the classical canonical model. If the accessibility relation R1 for 1 is the accessibility relation R2 for 2, then the axiomatic system for changes into S5.

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邓少波,黎敏,曹存根,眭跃飞.具有模态词□φ=1V2φ且可靠与完备的公理系统.软件学报,2015,26(9):2286-2296

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History
  • Received:June 23,2014
  • Revised:August 15,2014
  • Online: September 14,2015
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