Modeling Radical Indeterminacy in Branching Time Semantics

With the primary aim of preserving indeterminism and keeping the future open, several different branching time semantics have been proposed. The temporal frames on which these semantics are based are trees whose branches are typically endless. However, it is a genuine metaphysical possibility that the series of moments might come to an end. In light of this, a radical notion of indeterminacy can be adopted, one that is formally captured not merely by the branching of the future, but by a tree-like structure of time that, in addition to unbounded branches, also includes branches that terminate (dead branches). In this article, (i) we show how such a temporal frame can be formally developed, (ii) examine some implications of incorporating dead branches for both Peircean and Ockhamist branching time semantics, and (iii) outline a new semantics tailored to this kind of trees.