逻辑系统G3中命题的D-条件真度与近似推理

基于条件概率的思想,利用赋值集的随机化方法,在三值Gdel命题逻辑系统中引入公式的D-条件真度,证明了D-条件真度的MP规则和HS规则。引入公式间的D-条件相似度和D-条件伪距离,建立了D-条件逻辑度量空间,推导出D-条件伪距离的若干性质,证明了D-逻辑度量空间中二元运算“∨”,“∧”,“→”关于D-条件伪距离的连续性。在D-条件逻辑度量空间中提出了三种不同类型的近似推理模式并研究了它们之间的关系。

The D-conditional truth degree of formulas and approximate reasoning in the G3 propositional logic system

Based on conditional probability, using the randomization method of valuation set, the concept of D-conditional truth degree of formulas is introduced in the 3 valued Gdel propositional logic system. The MP rule and HS rule of D-conditional truth degrees are proved. The concepts of D-conditional similarity and D conditional pseudo distances between formulas are introduced and D-conditional logic metric space is built. Several properties of D-conditional pseudo distances are deduced and it is proved that the D-conditional pseudo-distances is continuous on the logical operation of “∨”, “∧”, “→” in D-conditional logic metric spaces. Three different types of approximate reasoning patterns are discussed in D-conditional logic metric space, and the relationships between them are studied.