Bisimulation through probabilistic testing
Information and Computation
Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Specifying coalgebras with modal logic
Theoretical Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
PSPACE Bounds for Rank-1 Modal Logics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A finite model construction for coalgebraic modal logic
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Expressivity of coalgebraic modal logic: the limits and beyond
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Admissibility of Cut in Coalgebraic Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Beyond rank 1: algebraic semantics and finite models for coalgebraic logics
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Cut elimination in coalgebraic logics
Information and Computation
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
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Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, become applicable to arbitrary rank 1 modal logics, without regard to their semantic status; we thus obtain purely syntactic versions of these results. As an extended example, we apply our framework to recently defined deontic logics.