Minimization for Kleene-Stone logic functions

Since the concept of fuzzy sets is proposed by L.A. Zadeh, as the extensions of Boolean functions many multiple-valued logic functions permitted to take truth values besides 0 and 1 have been investigated. Each one of multiple-valued logic functions motivated by the concept of fuzzy sets is one of the models of Kleene algebras, which have almost of the properties holding in Boolean algebras excluding the complementary laws. On the other hand, Kleene-Stone algebras have been proposed by G. Epstein and M. Mukaidono which have properties both Kleene algebras and Stone algebras. Therefore, it is considered that Kleene-Stone algebras correspond to non-classical logic system besides that of Kleene algebras. In the paper, we describe a typical example of Kleene-Stone algebras, which is called Kleene-Stone logic functions. Some properties of Kleene-Stone logic functions are clarified in the paper, especially an algorithm to derive a minimal form of a given Kleene-Stone logic function