模态逻辑公式的概率真度理论  

Theory of probability truth-degree for modal logic formulas

作　　者：李璧镜 LI Bi-jing(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2022年第3期1-5,11,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省教育厅专项科研项目(14JK1050)。

摘　　要：目的在模态逻辑系统中寻找一种广泛通用的公式真度理论框架,成为各种系统中已有真度理论的高度抽象或推广。方法从逻辑语构角度出发,将某一逻辑公式在特定环境下为真的程度看作是一个概率值,给出此概率值应该满足的公理刻画,并且结合不同逻辑系统自身的推理特点,寻找模态公式真度的内在关系性质。结果建立的真度理论分别在基本模态逻辑系统K、模态系统S4和S5中讨论分析了模态公式真度所满足的规律特征。结论不再受限于可能世界的有限性和概率测度空间的均匀性,进一步完善了模态公式的真度理论,为模态逻辑系统内进行近似推理提供了可行的模式。Purposes-To find a widely-used theoretical framework of formula truth-degree in modal logic system, which can become a highly abstract or essential generalization of formula truth-degree theory under various semantic backgrounds of all kinds of logic systems. Methods-From the perspective of the syntax, the truth-degree of modal formula defined by the axiomatic characterizations, is regarded as a probability value in the specific semantic background. Combined with the reasoning characteristics of different logic systems, the numerical relationship of the truth-degree of modal formula is compared. Results-The numerical laws and characteristics of the truth-degree of modal formula are discussed and analyzed in the basic modal logic system K, modal systems S4 and S5. Conclusions-The truth-degree theory of modal formula without the finite set of possible world and the uniform probability of measure space is established. It provides a feasible model for approximate reasoning in logic system.

关 键 词：模态逻辑 概率真度 相容 逻辑等价 

分 类 号：O141[理学—数学]