An analysis of first-order logics of probability
Artificial Intelligence
Bisimulation through probabilistic testing
Information and Computation
Alternating-time temporal logic
Journal of the ACM (JACM)
Modal Logic over Finite Structures
Journal of Logic, Language and Information
Homomorphism preservation theorems
Journal of the ACM (JACM)
Cut elimination in coalgebraic logics
Information and Computation
Rank-1 Modal Logics are Coalgebraic
Journal of Logic and Computation
ICLA'11 Proceedings of the 4th Indian conference on Logic and its applications
The Computer Journal
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Coalgebraic correspondence theory
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Coalgebraic predicate logic: equipollence results and proof theory
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
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We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for two natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, contrasting it with both coalgebraic modal logic and existing first-order proposals for special classes of Set-coalgebras (apart for relational structures, also neighbourhood frames and topological spaces). The semantic characterization of expressivity is based on the fact that our language inherits a coalgebraic variant of the Van Benthem-Rosen Theorem. Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes which allow for completeness--and in some cases beyond that.