一类一阶逻辑公式中的公理化真度理论及其应用

Let φ be the set consisting of all closed first-order formulas containing no function symbols. Based on the finite model and uniformly distributed probability theory, the present paper analyses a classic example in non-monotone logic, and proposes the truth degrees of conjunctions of universal closures of literals. Then the present paper establishes an axiomatic theory of truth degree on φ and proves that truth degrees of formulas in φ are computable. Moreover, this paper proves that the set H of truth degrees of formulas in φ coincides with the set of truth degrees of propositional formulas, and especially, truth degrees of universal closures of literals are equal to 1/2. Lastly, the present paper introduces the concepts of similarity degree and pseudo-metric between formulas of φ, and proposes the theory of consistency degree for logic theories. As an application, the consistency degree of a kind of Horn type data base is calculated.