一种泛逻辑代数系统  

A Kind of Algebraic Systems for Universal Logic

作　　者：罗敏霞[1] 何华灿[2] 

机构地区：[1]运城学院数学系,山西运城044000 [2]西北工业大学计算机学院,西安710072

出　　处：《计算机工程与应用》2005年第14期21-22,60,共3页Computer Engineering and Applications

基　　金：国家自然科学基金(编号:60273087);北京市自然科学基金(编号:4032009)资助

摘　　要：文[3]给出了理想状态(广义相关系数h=0.5,广义自相关系数k=0.5)下泛逻辑的形式演绎系统B,证明了此系统是可靠的。该文提出理想状态下(h=k=0.5)泛逻辑学对应的代数系统-UB代数,给出它的一系列性质。证明了UB代数是一个交换剩余半群;进一步证明了U B代数与M V代数、正规FI代数是等价的。The formal deductive system B of universal logic in the ideal condition(the generalized correlative coefficient h=0.5 and the generalized self-correlative coefficient k=0.5)has been given in paper3.We prove that the system B is sound.In this paper,we introduce UB algebras for universal logic in the ideal condition.Some properties are given.We prove that an UB algebra is a commutative residuated semigroup.Moreover,we show that an UB algebra,a MV algebra and a normal fuzzy implication algebra are equivalent.

关 键 词：UB代数 剩余半群 FI代数 MV代数 

分 类 号：O141.1[理学—数学]