Two Temporal Logics of Contingency

Abstract

This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named Ct, whose language includes a propositional constant and prove that (i) Ct is complete with respect to a certain class of general frames and (ii) the usual operators for past and future necessity are denable in such system. Furthermore, we will introduce the extension Ctlin that can be interpreted on linear and transitive general frames. The theoretical result of the current work is that contingency can be treated as a primitive notion in reasoning about temporal modalities.