中文摘要：

软件设计和硬件设计中经常遇见用逻辑方程或逻辑方程组表示的数学模型，讨论这类数学模型的求解问题是非常必要的。给出了AX=0，AX=1，AX=B AY=1（X中不含逻辑非变量，Y中含逻辑非变量）等类型的线性逻辑方程组有解、有惟一解的充分必要条件，讨论了解的个数并给出了求解公式或解集表示式，阐明了任何形式的逻辑方程或逻辑方程组都可转化为线性逻辑方程组求解。采用置换矩阵和极大项两种方法，系统全面地解决了线性逻辑方程组、一般逻辑方程和一般逻辑方程组的求解问题。

英文摘要：

The mathematical model represented by logical equation or logical equations is often used in the software and hardware design. It is necessary to discuss solutions for the mathematical models. The necessary and sufficient condition for linear logical equation such as AX=0, AX= 1, AX=B, AY= 1 （logic negation variables are not included in Xbut in Y） having solutions and having unique solution are obtained. The number of the solutions is discussed and the formula for solutions or expression of solution sets is given. The conclusion that the logical equation or logical equations in any form could be changed into linear logical equation is clarified. The two methods of permutation matrix and maximum item are employed for finding the solutions of linear logical equations, logical equation and logical equations.