On the α-superposition of functions of a k-valued logic

We reveal a relation between the operations of α-completion and closure for the systems of functions of a k-valued logic. For k = 3, 4 we construct the α-bases consisting of two binary operations. We prove that the complete system T of functions of a 4-valued logic containing all permutations of the set E4 = {0, 1, 2, 3} and the operation of addition modulo 4 is not α-complete, whereas its α-completion [Tα] will be an α-complete system.