| 逻辑系统G3在非均匀概率空间下命题的真度理论 |
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| 引用本文： | 左卫兵.逻辑系统G3在非均匀概率空间下命题的真度理论[J].数学研究,2008,41(2):205-211. |
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| 作者姓名： | 左卫兵 |
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| 作者单位： | 华北水利水电学院,数学与信息科学学院,河南,郑州,450011 |
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| 基金项目： | 河南省自然科学基金
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华北水利水电学院青年科学基金 |
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| 摘 要： | 在离散概率测度空间下定义了三值逻辑（p,q,r）测度，并相应地定义了命题逻辑系统中公式的真度概念；在三值逻辑（1/6．1/3．1/2）测度和（1/7．2/7.4/7）测度下证明了命题逻辑系统G3中全体公式的真度值之集在0．1]上是稠密的，并给出真度的表达式；利用真度定义公式的相似度和一种伪距离，为—般离散概率空间下三值命题的近似推理理论提供一种可能的框架．
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| 关 键 词： | 非均匀 概率空间 (p q r)测度 真度 相似度 |
On G(o)del 3-valued Truth Degree Theory in the Space of Uneven Discrete Probability |
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| Zuo Weibing.On G(o)del 3-valued Truth Degree Theory in the Space of Uneven Discrete Probability[J].Journal of Mathematical Study,2008,41(2):205-211. |
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| Authors: | Zuo Weibing |
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| Institution: | Zuo Weibing(Department of Mathematics and Information Science, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou Henan 450011) |
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| Abstract: | This paper defines the 3-valued （p, q, r） logic measure in the space of discrete probability, and correspondingly the truth degree of formula in proposition logic system. We also show that in the 3-valued （1/6.1/3.1/2） men,sure and （1/7.2/7.4/7） measure the truth degree of all formulas in the range of 0,1] is dense arid gives the expression of formula truth degree. Based on the similarity degree in the truth degree formulas. it educes a type of pseudo-distance in the set of all formulas, so provides a possible structure of proximity reasoning theory. |
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| Keywords: | uneven probability space （p q r） measure truth degree similarity degree |
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