Probabilistic logic metric and its application to approximate reasoning
The concepts of L probabilistic truth degree and L uncertainty degree are introduced in the paper. The conclusion that L probabilistic truth degree satisfies Kolmogorov axioms is reached by discussing some of their properties. The paper proves that the L uncertainty degree of conclusion is less than or equal to the sum of the product of L uncertainty degree of each premise and its essentialness degree in a formal inference. The L similarity degree and probabilistic logic pseudo metric between formulas are introduced by using the L uncertainty degree of formulas, and it indicates that there are not isolated points in the probabilistic logic pseudo metric space under some conditions. As an application, proposals of two different approximate reasoning models in the probabilistic logic pseudo metric space are raised as well as some examples to illustrate the practical application of these approximate reasoning models.