Theory of truth degree of modal logic formulas

Abstract

Abstract: This paper defines the perfect model and truth degree of modal formulas after analyzing the degree to modal logic and analyzing the theory of possible world. The conclusion is proved, that is, the truth degree of formulas without modal operators degenerates into a point and the value is equal to corresponding Borel degree.

Key words: modal logic system, modal formulas, Borel measure, truth degree

摘要： 在模态逻辑系统中，对可能世界进行了深入的分析，首次提出了完整模型的概念，并且在这个完整模型的框架下定义了模态公式的真度概念，建立了公式的真度理论。并且证明了：若模态公式[φ]不含任何模态词，即经典逻辑公式，它对应的模态真度[τ(φ)]就由区间退化为一个点，并且这个点就是该公式的Borel型真度值。

关键词: 模态逻辑系统, 模态公式, Borel测度, 真度

LI Bijing. Theory of truth degree of modal logic formulas[J]. Computer Engineering and Applications, 2013, 49(3): 40-43.

李璧镜. 模态逻辑公式的真度理论[J]. 计算机工程与应用, 2013, 49(3): 40-43.

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Theory of truth degree of modal logic formulas

模态逻辑公式的真度理论

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