Algebra for multiple valued logic systems

Abstract

An algebra for multiple valued logic systems is presented in this paper. This algebra uses r-1 new concurrent operators along with the traditional supremum and cycle operators. It is also shown that r+1 operators are required to generate any r-valued logic function. Five new theorems, similar to DeMorgan's Laws, are then used to show that only one fundamental mapping is sufficient to represent any multi-valued logic function.