本文提出新代数系统《,+,,,↑,0,*,1》。用此代数深入研究三值逻辑故障诊断。首先,在定义三值运算“↑”和三值异或“+”后,推出一些代数定理。在此基础上推出三值逻辑网络中任意类型故障诊断原理。然后引入“复阵列对”和“三值井运算”,将已用于二值逻辑网络中的方法推广到三值逻辑网络故障检测。 This paper proposes a new algebraic system “, + ,,, ↑, 0, *, 1”. Use this algebra to study the three-valued logic fault diagnosis. First of all, after defining the ternary operation “↑” and the ternary exclusive OR “+”, some algebraic theorems are introduced. On this basis, the principle of any type of fault diagnosis in three-valued logic network is introduced. Then we introduce “complex array pair” and “three-well operation” to generalize the methods that have been used in binary logic networks to three-valued logic network fault detection.