Studia Logica 84 (2):277-322 (2006)

Authors
Patrick Blackburn
Roskilde University
Abstract
In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language to the strong Priorean language . We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic
Keywords Hybrid logic  modal logic  nominals  axiomatisation  completeness  proof rules
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DOI 10.1007/s11225-006-9009-6
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Past, Present and Future.Arthur Prior - 1967 - Clarendon Press.
Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16 (1963):83-94.
Agency and Deontic Logic.John F. Horty - 2001 - Oxford University Press.

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Citations of this work BETA

A Logic for Diffusion in Social Networks.Zoé Christoff & Jens Ulrik Hansen - 2015 - Journal of Applied Logic 13 (1):48-77.
Completeness in Hybrid Type Theory.Carlos Areces, Patrick Blackburn, Antonia Huertas & María Manzano - 2014 - Journal of Philosophical Logic 43 (2-3):209-238.
The Logic of Imaginary Scenarios.Joan Casas-Roma, Antonia Huertas & M. Elena Rodríguez - 2020 - Logic Journal of the IGPL 28 (3):363-388.

View all 13 citations / Add more citations

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