Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
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
Semantical Principles in the Modal Logic of Coalgebras
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Logics Admitting Final Semantics
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
A compositional approach to defining logics for coalgebras
Theoretical Computer Science - Selected papers of CMCS'03
A Coalgebraic Perspective on Monotone Modal Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
A Coalgebraic Approach to Process Equivalence and a Coinduction Principle for Traces
Electronic Notes in Theoretical Computer Science (ENTCS)
ACM SIGACT News
A coalgebraic approach to the semantics of the ambient calculus
Theoretical Computer Science - Algebra and coalgebra in computer science
Modular Games for Coalgebraic Fixed Point Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Predicate Liftings Versus Nabla Modalities
Electronic Notes in Theoretical Computer Science (ENTCS)
Theoretical Computer Science
Bialgebraic methods and modal logic in structural operational semantics
Information and Computation
Rank-1 modal logics are coalgebraic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A computer-verified monadic functional implementation of the integral
Theoretical 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
Presenting functors by operations and equations
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Towards a coalgebraic semantics of the ambient calculus
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
The least fibred lifting and the expressivity of coalgebraic modal logic
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Modular algorithms for heterogeneous modal logics
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.