Handbook of logic in computer science (vol. 3)
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
From modal logic to terminal coalgebras
Theoretical Computer Science
Modal logic
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
Theoretical Computer Science - Selected papers of CMCS'03
Operations and equations for coalgebras
Mathematical Structures in Computer Science
Algebraic Semantics for Coalgebraic Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
A domain equation for bisimulation
Information and Computation
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
Duality for logics of transition systems
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
ACM SIGACT News
PSPACE bounds for rank-1 modal logics
ACM Transactions on Computational Logic (TOCL)
Rank-1 modal logics are coalgebraic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Coalgebraic modal logic in COCASL
WADT'06 Proceedings of the 18th international conference on Recent trends in algebraic development techniques
The goldblatt-thomason theorem for coalgebras
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Model constructions for moss' coalgebraic logic
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Presenting functors by operations and equations
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Testing semantics: connecting processes and process logics
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
VoCS'08 Proceedings of the 2008 international conference on Visions of Computer Science: BCS International Academic Conference
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
A Characterisation of Expressivity for Coalgebraic Bisimulation and Simulation
Electronic Notes in Theoretical Computer Science (ENTCS)
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This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is well-known that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the other hand, do provide an adequate semantics for finitary modal logics. This leads us to study the relationship of finitary modal logics and Set-coalgebras by uncovering the relationship between Set-coalgebras and Stone-coalgebras. This builds on a long tradition in modal logic, where one studies canonical extensions of modal algebras and ultrafilter extensions of Kripke frames to account for finitary logics. Our main contributions are the generalisations of two classical theorems in modal logic to coalgebras, namely the Jónsson-Tarski theorem giving a set-theoretic representation for each modal algebra and the bisimulation-somewhere-else theorem stating that two states of a coalgebra have the same (finitary modal) theory iff they are bisimilar (or behaviourally equivalent) in the ultrafilter extension of the coalgebra.