Temporal necessity and the conditional

Abstract

In [12] Richmond Thomason and Anil Gupta investigate a semantics for conditional logic that combines the ideas of [8] and [9] with a branching time model of tense logic. The resulting branching time semantics for the conditional is intended to capture the logical relationship between temporal necessity and the conditional. The central principle of this logical relationship is Past Predominance, according to which past similarities and differences take priority over future similarities and differences in determining the comparative similarity of alternative possible histories with respect to a given present moment.

In this paper I will use ordinary possible worlds semantics (i.e. Kripke frames) to solve the completeness problem for a system of logic that combines conditional logic with temporal necessity in the context of Past Predominance. Branching time models turn out not to be necessary for the articulation of Past Predominance, and this means that one can axiomatize Past Predominance without first having to solve a much more difficult problem: the completeness problem for the logic of temporal necessity in the context of branching time.

Thomason and Gupta argue in [12] that in addition to Past Predominance, temporal necessity and the conditional are logically related, by what have become known as the Edelberg Inferences, whose apparent validity motivates the very complicated theory presented at the end of [12]. I will conclude this paper by examining how the Edelberg inferences would be incorporated into the possible worlds based system presented in the earlier sections of this paper.