Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (6): 37-41.DOI: 10.3778/j.issn.1002-8331.2010.06.011

• 研究、探讨 • Previous Articles     Next Articles

Theory of probability truth degree in £ukasiewicz 3-valued logic system

GUAN Xiao-hong,LIU Xiao   

  1. Department of Mathematics and Information Science,Henan Normal University,Xinxiang,Henan 453007,China
  • Received:2008-09-19 Revised:2008-12-12 Online:2010-02-21 Published:2010-02-21
  • Contact: GUAN Xiao-hong


关晓红,刘 晓   

  1. 河南师范大学 数学与信息科学学院,河南 新乡 453007
  • 通讯作者: 关晓红

Abstract: Using the infinite product of unevenly distributed probability space ,this paper introduces the theory of probability truth degree in £ukasiewicz 3-valued propositional logic.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.

Key words: probability measure, probability truth degree, similarity degree, pseudo-metric, isolated point

摘要: 利用势为3的非均匀概率空间的无穷乘积,在£ukasiewicz三值命题逻辑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。

关键词: 概率测度, 概率真度, 相似度, 伪距离, 孤立点

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