CHARACTERIZATION OF MONOTONIC MULTIPLE-VALUED FUNCTIONS AND THEIR LOGIC EXPRESSIONS

This paper presents some fundamental properties of multiple-valued log ic functions monotonic in a partial-ordering relation which is introdu ced in the set of truth values and does not necessarily have the great est or least element. Two kinds of necessary and sufficient conditions for monotonic p-valued functions are given with the proofs. Their log ic formulas using unary operators defined in the partial-ordering rela tion and a simplification method for those logic formulas are also giv en. These results include as their special cases our former results fo r p-valued functions monotonic in the ambiguity relation which is a pa rtial-ordering relation with the greatest element.