Similarity Degree, Pseudo-metric And Approximate Reasoning In Propositional Logic System

Artificial Intelligence is a valued research field and inference is active in it. The inference of traditional computer is designed by two-value logic system. It is the approximate reasoning that the intelligence computer should use. It is very important to compute the distance between two formulas in approximate reasoning. This dissertation begins with the research of similarity degree, then pseudo-metric and approximate reasoning in propositional logic system are studied.Chapter one: Preliminary. The five components of propositional logic system and three logic systems, namely, classical two-value logic system, Lukasiewicz n-value logic system, R₀ n-value logic system are introduced.Chapter two: The concept of truth degree, similarity degreeξ₁,ξ₂ and regular similarity degree in classical two-value logic system are introduced. The definition of regular similarity is simplified and the definition of the semi-regular similarity degree and a new similarity degreeξ₀ are given. Also, we proved the fact thatξ₀ andξ₁ are regular similarity degree in classical two-value logic system, andξ₀ is semi-regular similarity degree in 2n-value logic system.Chapter three: First, we induce three pseudo-metric spaces from the three similarity degree. Then, an order was defined on the three different pseudo-metrics. Finally the fact that the three different pseudo-metrics are topological isomorphic is proved.Chapter four: We give the concept of divergence degree in L , L_n, L*_n. In order to solve Professor Wang Guojun's open question of the relationship between the three errors of approximate reasoning in n-value logic system, we first change the three errors to three distances in propositional logic system, then we figure out the result that the three distances are equal, finally we prove the equivalence of the three errors in propositional logic system. Hence, the open question is partly solved.