Logic Journal of the IGPL 15 (1):53-76 (2007)

Valentin Goranko
Stockholm University
This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees
Keywords branching time temporal logics  linear orders  trees  Peircean semantics  Ockhamist semantics  transfer of definability
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DOI 10.1093/jigpal/jzl035
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References found in this work BETA

Modal and Temporal Logics.Colin P. Stirling - 1991 - LFCS, Department of Computer Science, University of Edinburgh.

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Citations of this work BETA

First-Order Aspects of Tree Paths.Ruaan Kellerman - 2015 - Logic Journal of the IGPL 23 (4):688-704.

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