Fundamental properties of multivalued kleenean functions

Abstract

In the real world, there are many propositions which cannot be determined to be true or false. In order to treat such propositions, multivalued logic systems which are permitted to take more than true (1) or false (0) values have been developed. In this paper, we will describe fundamental properties of multivalued Kleenean functions, which are effective for treating ambiguity. First, we will introduce a partial order relation into the set of truth values {0, 1/(m - 1), …, (m - 2)/(m - 1), 1}. It will be shown that any multivalued Kleenean function is monotone for this partial order relation. Next, it will be shown that any multivalued Kleenean function can be determined uniquely for inputs {0, 1/2, 1} only. Finally, we will describe P-type logic functions for multivalued Kleenean functions which are capable of correcting input failures.