10.4230/LIPICS.STACS.2009.1855
Schröder, Lutz
Lutz
Schröder
Pattinson, Dirk
Dirk
Pattinson
Strong Completeness of Coalgebraic Modal Logics
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2009
Logic in computer science
Semantics
Deduction
Modal logic
Coalgebra
Albers, Susanne
Susanne
Albers
Marion, Jean-Yves
Jean-Yves
Marion
2009
2009-02-19
2009-02-19
2009-02-19
en
urn:nbn:de:0030-drops-18559
10.4230/LIPIcs.STACS.2009
978-3-939897-09-5
1868-8969
10.4230/LIPIcs.STACS.2009
LIPIcs, Volume 3, STACS 2009
26th International Symposium on Theoretical Aspects of Computer Science
2013
3
55
673
684
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Albers, Susanne
Susanne
Albers
Marion, Jean-Yves
Jean-Yves
Marion
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2009
3
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
134937 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties - up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a generic canonical model construction in the semantic framework of coalgebraic modal logic, which pinpoints coherence conditions between syntax and semantics of modal logics that guarantee strong completeness. We apply this method to reconstruct canonical model theorems that are either known or folklore, and moreover instantiate our method to obtain new strong completeness results. In particular, we prove strong completeness of graded modal logic with finite multiplicities, and of the modal logic of exact probabilities.
LIPIcs, Vol. 3, 26th International Symposium on Theoretical Aspects of Computer Science, pages 673-684