经典命题逻辑中公式的Γ-随机真度与近似推理

The Γ-rand Truth Degree of Fomulas and Approximate Reasoning in Classical Propositional Logic

利用概率空间的无穷乘积,在经典二值命题逻辑中引入了公式的Γ-随机真度概念以及公式间的Γ-相似度概念。进而导出了全体公式集上的一种伪距离,建立了逻辑度量空间。最后提出了基于Γ-随机真度的三种不同的近似推理模式,并且证明了这三种近似推理模式之间是相互等价的。

By means of the infinite product of probability spaces, this paper introduces the Г-rand truth degree of formulas and Г-similarity degree of two formulas in classical propositional logic. Moreover, a pseudo-metric on the set of formulas is introduced. Thus a logical metric space is established. Finally, we give three patterns of approximate reasoning based on Г-rand truth degree and it is proved that they are equivalent.