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.

The paper concerns time, change and contradiction, and is in three parts. The first is an analysis of the problem of the instant of change. It is argued that some changes are such that at the instant of change the system is in both the prior and the posterior state. In particular there are some changes from p being true to p being true where a contradiction is realized. The second part of the paper specifies a formal logic which accommodates (...) this possibility. It is a tense logic based on an underlying paraconsistent prepositional logic, the logic of paradox. (See the author's article of the same name Journal of Philosophical Logic 8 (1979).) Soundness and completeness are established, the latter by the canonical model construction, and extensions of the basic system briefly considered. The final part of the paper discusses Leibniz's principle of continuity: Whatever holds up to the limit holds at the limit. It argues that in the context of physical changes this is a very plausible principle. When it is built into the logic of the previous part, it allows a rigorous proof that change entails contradictions. Finally the relation of this to remarks on dialectics by Hegel and Engels is briefly discussed. (shrink)