四值Gdel命题逻辑系统中公式的概率真度理论

Theory of Probability Truth Degree in Gdel 4-valued Propositional Logic System

在四值Gdel命题逻辑系统中提出了公式的概率真度,证明了全体公式的概率真度值之集在[0,1]中没有孤立点;定义了两个公式间的概率相似度,建立了概率逻辑度量空间,证明了此空间中没有孤立点,为研究四值Gdel命题逻辑系统的近似推理提供了思路。

This paper proposed the theory of probability truth degree in Godel 4-valued propositional logic. It is proved that the set of probability truth degree of all formulas has no isolated point in [0,1]. The conceptions of probability similarity degree on two formulas were defined. Moreover, the probability logic metric space was built. It was proved that this space has no isolated point. Then it can provide the thought for approximate reasoning theory.