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

Published online by Cambridge University Press:  12 March 2014

Alberto Zanardo
Alberto Zanardo*
Affiliation:
Dipartimento Di Matematica P. A., Università Di Padova, Via Belzoni 7, I-35131 Padova, Italy, E-mail: alberto@pdmat1.math.unipd.it
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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 〈moment, history〉 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 1 - 39
Copyright
Copyright © Association for Symbolic Logic 1996

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