Fundamental properties of extended Kleene-Stone logic functions

Abstract

In order to treat modality (necessity, possibility) in fuzzy logic, the intuitionistic logical negation is required. Infinite multivalued logic functions that introduce the intuitionistic logical negation into fuzzy logic functions are called Kleene-Stone logic functions, and they make it possible to treat modality. The domain in which Kleene-Stone logic functions can handle modality, however, is too limited. The authors define alpha -KS logic functions as infinite multivalued logic functions using a unary operation instead of the intuitionistic logical negation of Kleene-Stone logic functions. Some algebraic properties of alpha -KS logic functions are demonstrated, and a necessary and sufficient condition for a seven-valued logic function to be an alpha -KS logic function is shown.<>