Quantification over sets of possible worlds in branching-time semantics

Studia Logica 82 (3):379 - 400 (2006)
Abstract
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 quantification over histories, which is a second-order quantification 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 first-order counterparts of the original semantics.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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Leon Henkin (1950). Completeness in the Theory of Types. Journal of Symbolic Logic 15 (2):81-91.

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