Characterization of Monotonic Multiple-Valued Functions and Their Logic Expressions

摘要

This paper presents some fundamental proper- ties of multiple-valued logic functions monotonic in a partial- ordering relation which is introduced in the set of truth values and does not necessarily have the greatest or least element. Two kinds of necessary and sufficient conditions for monotonic p- valued functions are given with the proofs. Their logic formulas using unary operators defined in the partial-ordering relation and a simplification method for those logic formulas are also given. These results include as their special cases our former results for p-valued functions monotonic in the ambiguity relation which is a partial-ordering relation with the greatest element.