Many-Valued Logics

Abstract

Throughout this chapter, we shall assume that k is a natural number larger than 2. We shall denote the set {0, 1,..., k − 1} by E k . The function f(x n ) = f(x 1, x 2,...,x n ) is called a function of the k-valued logic if, on any tuple α = (α 1, α2,..., α n ) of values of the variables x 1, x 2,..., x n , where α1 ∈ E k , the value f(a) also belongs to the set E k . The set of all functions of the k-valued logic is denoted by P k . The concept of fictitious and essential variables, equal functions, formulas generated by a set of functions (and connectives), superposition and closure operations, closed class, basis, etc., are defined in k-valued logic in the same way as in Boolean algebra. Hence, we shall give only the definitions of such concepts that differ essentially from the corresponding concepts in P 2.