Journal of Software:2018.29(10):3091-3110

(陕西师范大学 数学与信息科学学院, 陕西 西安 710119;陕西科技大学 文理学院, 陕西 西安 710021)
The Hamming Distance Representation and Decomposition Theorem of Formula's Truth Degree
YU Peng,ZHAO Bin
(School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China;School of Arts and Sciences, Shaanxi University of Science and Technology, Xi'an 710021, China)
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Received:December 12, 2016    Revised:June 19, 2017
> 中文摘要: 首先应用模糊集截集的方法,给出了多值逻辑系统Łn中广义重言式的一个等价刻画,并利用模糊集间的标准Hammin距离,定义了公式间的Hamming距离、Hamming相似度与Hamming真度,给出了计量逻辑学基本概念的Hamming距离表示方法.然后给出了计量逻辑学中公式真度的一个分解定理,这个定理指出在计量逻辑学中,任意一个公式的真度等于一些互不相容的公式的真度之和,而公式φ本身则逻辑等价于这些公式的并.最后应用所提方法定义了广义MP问题的三-I真度解,并讨论了三-I真度解的存在性问题.
Abstract:First in this paper, an equivalent characterization of generalized tautologies in Łn is introduced by using the method of cut of fuzzy set, the Hamming distance, Hamming similarity degree and Hamming truth degree between formulas are defined by means of standard Hamming distance between fuzzy sets, and Hamming distance representation of the basic concepts of quantitative logic is described. Then, the truth degree decomposition theorem of formula in quantitative logic is presented. This theorem points out that in quantitative logic, the truth degree of any formula φ is equal to the sum of the truth degrees of some incompatible formulas, and the formula φ itself is logically equivalent to the join of these formulas. Finally, the problem of triple-I truth degree solution of the generalized MP problem is proposed, and the existence of the triple-I truth degree solution is discussed.
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基金项目:国家自然科学基金(11531009);中央高校基本科研业务费专项资金(GK201501001) 国家自然科学基金(11531009);中央高校基本科研业务费专项资金(GK201501001)
Foundation items:National Natural Sciences Foundation of China (11531009); Fundamental Research Funds for the Central Universities (GK201501001)
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YU Peng,ZHAO Bin.The Hamming Distance Representation and Decomposition Theorem of Formula's Truth Degree.Journal of Software,2018,29(10):3091-3110