A universal theory of measure and integral on valuation spaces with respect to diverse implication operators

作     者：王国俊 

作者机构：Institute of Mathematics Shaanxi Normal University Xi'an 710062 China 

出 版 物：《Science China(Technological Sciences)》 (中国科学（技术科学英文版）)

年 卷 期：2000年第43卷第6期

页      面：586-594页

核心收录：

学科分类：0810[工学-信息与通信工程] 07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0701[理学-数学] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：implication operator valuation space Lebesgue measure and integral t(α-tautology) truth de-gree universal logical metric space approximate reasoning. 

摘      要：Valuation spaces with respect to diverse implication operators are investigated in a unified way where the Lebesgue measure is a commonly used measure, and it is proved that all the logic formulas are measurable functions with respect to popularly used implication operations. The concept of t-(α-tautology) is introduced and rules of generalized modus ponens (MP) and hypothetic syllogism (HS) are established in the sense of semantics. The concept of truth degree of a logic formula is introduced and rules of integral MP and integral HS are proposed. Finally, a kind of pseudo-metric is introduced to the set consisting of all logic formulas by establishing a universal logical metric space, making it possible to develop a new type of approximate reasoning arise.