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This paper investigates the general logical expression of k-valued and mix-valued pseudo-logical functions. First, by constructing multi-valued logical operators, we present the general logical expression of k-valued pseudo-logical functions. Second, we consider the most general case of mix-valued, and establish the logical expression of mix-valued pseudo-logical functions. Finally, we convert the pseudo-logical function into an algebraic form by using the semi-tensor product. Two illustrative examples are studied to demonstrate the corresponding theoretical results.