标准序列逻辑系统S_3中的相似度及伪距离

Similarity degree and pseudo-distance in propositional logic S_3

在三值标准序列逻辑系统中引入了公式的真度概念,并利用真度定义了公式间的相似度,进而导出全体公式集上的一种伪距离,证明了伪距离空间中没有孤立点,从而可以考虑用一列公式去逼近某个公式,这就为进一步在三值标准序列逻辑系统中展开近似推理奠定了基础.

A concept of truth degrees of a formula in 3-valued prepositional logic S3 is given and,hence,the similarity degree between formulas is also defined.Further,a kind of pseudo-distance in the set of all formulas is derived and it is proved that the pseudo-distance space has no singularity,so that certain formula can be conceivably approximated by a series of formula,paving a way for further study of approximate reasoning.