| 标准序列逻辑系统S_3中公式的概率真度理论 |
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| 引用本文： | 关晓红,李骏.标准序列逻辑系统S_3中公式的概率真度理论[J].模糊系统与数学,2009,23(6). |
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| 作者姓名： | 关晓红 李骏 |
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| 作者单位： | 1. 河南师范大学,数学与信息科学学院,河南,新乡,453007
2. 兰州理工大学,理学院,甘肃,兰州,730050 |
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| 基金项目： | 国家自然科学基金资助项目，河南省教育厅自然科学研究计划项目 |
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| 摘 要： | 利用势为3的非均匀概率空间的无穷乘积在三值标准序列逻辑系统中引入了公式的概率真度概念,证明了全体公式的概率真度值之集在0,1]中没有孤立点;利用概率真度定义了概率相似度和伪距离,进而建立了概率逻辑度量空间,证明了该空间中没有孤立点,为三值命题的近似推理理论提供了一种可能的框架.
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| 关 键 词： | 概率测度 概率真度 相似度 伪距离 孤立点 |
The Theory of Probability Truth Degree in Standard Serial Logic System S_3 |
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| GUAN Xiao-hong,LI Jun.The Theory of Probability Truth Degree in Standard Serial Logic System S_3[J].Fuzzy Systems and Mathematics,2009,23(6). |
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| Authors: | GUAN Xiao-hong LI Jun |
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| Abstract: | Based on the infinite product of unevenly distributed probability space, this paper introduced the theory of probability truth degree in 3-valued propositional logic S_3. It is proved that the set of probability truth degree of all formulas has no isolated point in 0,1]. The conceptions of probability similarity degree and pseudo-metric on two formulas are defined by means of the concept of probability truth degree of propositions.Moreover,the probability logic metric space is built. It is proved that this space has no isolated point. Then it can provide a possible framework for approximate reasoning theory. |
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| Keywords: | Probability Measure Probability Truth Degree Similarity Degree Pseudo-metric Isolated point |
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