一类一阶逻辑公式中的公理化真度理论及其应用  

Axiomatic theory of truth degree for a class of first-order formulas and its application

作　　者：王国俊[1] 

机构地区：[1]陕西师范大学数学研究所,西安710062

出　　处：《中国科学：信息科学》2012年第5期648-662,共15页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:10771129;11171200)资助项目

摘　　要：设Φ是全体不含函数符号的一阶闭逻辑公式之集.本文基于有限模型和均匀概率的思想对非单调逻辑中的典型案例做了分析,通过概率计算给出了应当赋予文字的完全闭包及其合取的真度值.以此为基础,在Φ中建立了公理化的真度理论.证明了Φ中每个公式的真度都是可计算的,并且证明了Φ中逻辑公式的真度之集H与命题逻辑中的计算结果相一致,特别是其中所有闭文字的真度都等于1/2.在真度理论的基础上引入了Φ中公式之间相似度和伪距离的计算方法,并提出了逻辑理论的相容度理论.作为应用,给出了估计Horn子句型数据库相容度的一种方法.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 anMyses 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 φcoincides 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.

关 键 词：谓词逻辑 一阶逻辑公式 函数符号 真度 可计算性 HORN子句 

分 类 号：O141[理学—数学]