Note on a six-valued extension of three-valued logic

Abstract

In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's “useful” four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.