Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Automata and Algebras in Categories
Automata and Algebras in Categories
Automata for the Modal mu-Calculus and related Results
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Category Theory and Computer Science
Semantics of Name and Value Passing
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Coalgebraic modal logic: soundness, completeness and decidability of local consequence
Theoretical Computer Science
A hierarchy of probabilistic system types
Theoretical Computer Science - Selected papers of CMCS'03
Stochastic Relations
Expressivity of coalgebraic modal logic: The limits and beyond
Theoretical Computer Science
Predicate Liftings Versus Nabla Modalities
Electronic Notes in Theoretical Computer Science (ENTCS)
Completeness for flat modal fixpoint logics
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Exemplaric Expressivity of Modal Logics
Journal of Logic and Computation
Presenting functors by operations and equations
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
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Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss's coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in Raul Andres Leal (2008) [34] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatisation of Moss's logic. The three logics are equivalent for a natural but restricted class of functors. We give examples showing that the logics differ in general. Finally, we argue that the quest for a generic logic for T-coalgebras is still open in the general case.