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Journal of Logic and Computation 2006 16(2):161-175; doi:10.1093/logcom/exi086
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Vol. 16 No. 2, © The Author, 2006. Published by Oxford University Press. All rights reserved.

Original Articles

Hybrid Logics with Infinitary Proof Systems

Barteld Kooi1, Gerard Renardel de Lavalette2 and Rineke Verbrugge3

1 Department of Philosophy, University of Groningen, 9700 AB Groningen, The Netherlands. Email: b.p.kooi{at}rug.nl, 2 Department of Computing Science, University of Groningen, 9700 AB Groningen, The Netherlands. Email: g.r.renardel.de.lavalette{at}rug.nl, 3 Department of Artificial Intelligence, University of Groningen, 9700 AB Groningen, The Netherlands. Email: rineke{at}ai.rug.nl

We provide a strongly complete infinitary proof system for hybrid logic. This proof system can be extended with countably many sequents. Thus, although these logics may be non-compact, strong completeness proofs are provided for infinitary hybrid versions of non-compact logics like ancestral logic and Segerberg's modal logic with the bounded chain condition. This extends the completeness result for hybrid logics by Gargov, Passy, and Tinchev.

Keywords: Hybrid logic, strong completeness, non-compact logics, infinitary proof rules

Received 1 March 2005.


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