In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the moment-history pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of so-called transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open at a branching point. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. In addition to temporal and modal operators, a so-called stability operator becomes interpretable as a universal quantifier over the possible future extensions of a given transition set. The stability operator allows us to specify how and how far time has to unfold for the truth value of a sentence at a moment to become settled and enables a perspicuous treatment of future contingents. We show that the semantics developed along those lines generalizes and extends extant approaches: both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only, and on both accounts, stability collapses into truth.
Keywords Branching time  Transitions  Stability  Future contingents
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DOI 10.1007/s10849-015-9231-6
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References found in this work BETA

Past, Present and Future.Arthur N. Prior - 1967 - Oxford, England: Clarendon Press.
Time and Modality.Arthur N. Prior - 1955 - Greenwood Press.
Past, present and future.Arthur Prior - 1967 - Revue Philosophique de la France Et de l'Etranger 157:476-476.

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Citations of this work BETA

First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
B-Theory and Time Biases.Sayid Bnefsi - 2019 - In Patrick Blackburn, Per Hasle & Peter Øhrstrøm (eds.), Logic and Philosophy of Time: Further Themes from Prior. Aalborg, Denmark: Aalborg University Press. pp. 41-52.
Temporal Logic.Antony Galton - 2008 - Stanford Encyclopedia of Philosophy.

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