n值Lukasiewicz命题逻辑系统中公式的随机真度及近似推理

The Randomized Truth Degree of Formulas and Approximate Reasoning in n-valued Lukasiewicz Propositional Logic System

利用赋值集的随机化方法,在n值Lukasiewicz命题逻辑系统中引入公式的随机真度,证明了随机真度的MP规则、HS规则及交推理规则;同时引入公式间的随机相似度和随机伪距离,建立了随机逻辑度量空间,推导出随机相似度的若干性质,证明了随机逻辑度量空间中逻辑运算的连续性;并在随机逻辑度量空间中提出了三种不同类型的近似推理模式,证明了三种近似推理模式的等价性.

Using the randomization method of valuation set,the concept of randomized truth degree of formulas is introduced into n-valued Lukasiewicz propositional logic system. The MP rule,HS rule and meet inference rules of randomized truth degree are proved. At the meantime,the concept of randomized similarity and randomized pseudo-distances between formulas are introduced and the randomized logic metric space is built.Several properties of randomized similarity are deduced to prove the continuity of logical operations in this space.Three different types of approximate reasoning patterns are introduced in randomized logic metric space.And they are proved to be equivalent.