Quantification over Sets of Possible Worlds in Branching-Time Semantics

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quanti¯cation over histories, which is a second-order quanti¯cation over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as ¯rst-order counterparts of the original semantics.