R_0-代数上的距离结构及其在命题逻辑中的应用

Metric Structures on R_0-Algebras and an Application to Propositional Logic

设Ω是全体从R0-代数M到R0单位区间[0,1]的同态之集,μ是Ω上的一概率测度。引进M上的元素的尺寸和元素对间的相似度,然后在M上建立了伪距离。作为应用,将距离R0-代数理论应用到命题逻辑的近似推理理论。

Let Ω be the set of all homomorphisms from the R0-algebra M into the R0-unit interval [0, 1], and μ be a probability measure on Ω. The concepts of sizes of elements of M and similarity degrees of pairs of elements of M with respect to μ are introduced, and then a pseudo-metric on M is defined therefrom. As an application, metric R0-algebra theory is applied to approximate reasoning theory of propositional logic.