Theory of completeness is essential for multi-valued logical functions. Using semi-tensor product (STP) of matrices, the algebraic form of k-valued logical functions is presented. Using algebraic form, a method is proposed to construct an adequate set of connectives (ASC), consisting of unary operators with conjunction/disjunction for k-valued logical functions, which can be used to express any k-valued logical functions. Based on it, two normal forms of k-valued logical functions are presented, which are extensions of the disjunctive normal form and conjunctive normal form of Boolean functions respectively. The ASC is then simplified to a condensed set. Finally, the normal forms are further extended to mix-valued logical functions.

完整性理论对于多值逻辑功能至关重要。使用矩阵的半张量积（STP），给出了k值逻辑函数的代数形式。使用代数形式，提出了一种构建足够的连词集（ASC）的方法，该连词集由一元运算符组成，带有用于k值逻辑函数的合取/析取，可以用来表示任何k值逻辑函数。在此基础上，提出了k值逻辑函数的两种范式，分别是布尔函数的析取范式和联合范式的扩展。然后将ASC简化为一个精简集合。最后，范式进一步扩展到混合值逻辑函数。