Two Temporal Logics of Contingency

Matteo Pascucci

Abstract


This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named {\bf{C}}$_t$, whose language includes a propositional constant and prove that (i) {\bf{C}}$_t$ is complete with respect to a certain class of general frames and (ii) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension  {\bf{C}}${_t}lin$ 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.

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