Branching-time logic with quantification over branches: The point of view of modal logic

Journal of Symbolic Logic 61 (1):1-39 (1996)

Abstract
In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (3-modal) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames
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DOI 10.2307/2275595
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Branching Space-Time.Nuel Belnap - 1992 - Synthese 92 (3):385 - 434.
Formal Properties of 'Now'.Hans Kamp - 1971 - Theoria 37 (3):227-273.
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Time and Modality in the Logic of Agency.Brian F. Chellas - 1992 - Studia Logica 51 (3-4):485 - 517.

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