二值命题逻辑中的蕴涵度量与近似推理

The Implication Measurement and Approximate Reasoning in Two-valued Propositional Logic

在二值命题逻辑系统中引入公式的真度、条件真度和蕴涵真度概念,为二值命题逻辑系统的程度化研究和近似推理提供了数值化工具。为了讨论基于真度、条件真度和蕴涵真度的近似推理模式的关系问题,以真度概念为基础,在二值命题逻辑系统中引入蕴涵度量概念,并通过蕴涵度量的真度表示式,给出了与有限理论相关的分别基于真度、条件真度和蕴涵真度的伪距离的蕴涵度量表示式,证明了分别基于真度、条件真度和蕴涵真度的近似推理问题可以转化为基于蕴涵度量的近似推理讨论,并给出了蕴涵度量在近似推理中的应用,为二值命题逻辑系统的基于不同真度的近似推理研究提供数值化方法。

Based on the truth degree of the formula, conditional truth degree and the implicative truth degree respectively, we gain the new numerical studying method of the severity of the systems and the approximate reasoning problems in the two-valued propositional logic. Furthermore, we also concentrate on the relationship among the truth degree, conditional truth degree and the implicative truth degree in approximate reasoning mode. According to the truth degree in this paper, we obtain the definition of the implication measurement in the two-valued propositional logic system. Using the truth degree expressions of the implication measurement, we show the implication measurement expressions of the pseudo metric which are resulted separately from the truth degree, conditional truth degree and implicative truth degree. These expressions are all relative to the finite theory. Hence we have achieved the transformation from the problems of approximate reasoning based on the three kinds of truth degrees as above to the approximate reasoning based on the implication measurement. Meanwhile, we have mastered the applications of approximate reasoning in implication measurement. So these studies could become the numerical identification of approximate reasoning which is based on the different kinds of truth degree in two-valued propositional logic.