代数替换公理与对偶原理  

Algebraic Substitution Axiom and the Principle of Duality

作　　者：史天治[1] 

机构地区：[1]淮阴师范学院物理与电子学系,江苏淮安223001

出　　处：《重庆文理学院学报（自然科学版）》2007年第2期7-11,共5页Journal of Chongqing University of Arts and Sciences

摘　　要：提出和阐明了两个普遍的逻辑规律——代数替换公理与对偶原理．通过这两个规律,极大地简化和统一了布尔代数中的运算规律和运算公式．在布尔代数中,A的非与A的对偶本质上是一回事．对偶本质上是一种对称的关系．一个代数表达式(这里的表达式是一个广义的概念,它可以是一个变量,一个常量,一个逻辑函数,一个集合表达式等)的对偶,等于该表达式中的每个元素(如变量、常量、运算符、关系符等,对偶算子除外)分别同时取其对偶,并保持原来的运算次序不变(也即原表达式中的对偶算子和括号位置不变);对于关系表达式而言,原表达式与其对偶表达式必然同时正确或同时错误,这一规律叫做对偶原理．The article puts forward and sets out clearly algebraic substitution axiom and the principle of duality, which are both universal logic laws. By using these two laws, the article simplifies and unifies greatly the operation rules and formulas in Boolean algebra. In Boolean algebra, the dual of A is equal to NOT A. Dual is a kind of symmetrical relation. The dual of an expression is equal to making the dual of every elementary symbol simultaneously（ dual operator and parentheses excluded）, keeping the original operation priority unchanged; meanwhile, if a relational expression is right, the dual of it must be right, vice versa; this law is called the principle of duality.

关 键 词：布尔代数 对偶原理 对偶算子 代数替换公理 

分 类 号：O153.2[理学—数学] TP302.2[理学—基础数学]