Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Equational and implicational classes of coalgebras
Theoretical Computer Science
Equational axiomatizability for coalgebra
Theoretical Computer Science
Modal logic
Automata and Algebras in Categories
Automata and Algebras in Categories
Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Category Theory and Computer Science
The logic of public announcements, common knowledge, and private suspicions
The logic of public announcements, common knowledge, and private suspicions
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
ACM SIGACT News
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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We show how coalgebras can be presented by operations and equations. This is a special case of Linton's approach to algebras over a general base category ${\cal X}$, namely where ${\cal X}$ is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic. This relies on the fact that coalgebraic operations respect an appropriate notion of bisimulation and can be considered as modal operators.