Modalities in Temporal Logic

In logics of branching-time, ‘possibility’ can be conceived as ‘existence of a suitable set of histories’ passing through the moment under consideration. A particular limit case of this is the Ockhamist notion of possibility, which is explained as truth at some history. The tree-like representation of time offers other ways of defining possibility as, for instance, truth at any history in some equivalence class modulo undividedness. In general, we can consider representations of time in which, at any moment t, the set of histories passing through t can be decomposed into indistinguishability classes. This yields to a new general notion of possibility including, as particular cases, other notions previously considered.