n元三值函数可由L3^＊中公式导出的充要条件  

Sufficient and Necessary Condition of Three Valued Function with n Variables Being Induced by a Formula of L3~＊

作　　者：王永安[1] 

机构地区：[1]西安文理学院数学系,710065

出　　处：《西安工业大学学报》2009年第5期500-504,共5页Journal of Xi’an Technological University

基　　金：国家自然科学基金资助项目(10331010)

摘　　要：三值Lukasiewicz命题逻辑L3*中的任何公式的赋值均为0,1/2,1中的某个元素.0,1/2,1及其上定义的运算■,→构成三元MV代数.根据规定的0,1/2,1中元素之间运算∧,∨,■,→的特点,构造性地证明了对于给定的n元三值函数f∶0,1/2,1n→0,1/2,1,当且仅当f满足一定条件时,f均可由L3*中的公式导出.The assignment of any formula of three-valued Lukasienicz propositional logic L3^＊ is one of the elements in set 0,1/2,1.set {0,1/2,1} with the operation ,→ on it constitutes three- element MV algebra.According to the character of operations ∧,∨, ,→ among elements of set 0,1/2,1,it is constructively proved that for a given function f∶0,1/2,1n→0,1/2,1,it can be induced from a formula of three-valued lukasiewicz propositional logic L3^＊ if and only if it satisfies certain conditions.

关 键 词：三值Lukasiewicz命题逻辑L3* 三元MV代数 函数f∶0 1/2 1n→0 1/2 1 导出函数 充要条件 

分 类 号：O141.1[理学—数学]