Topology via logic
Information systems for continuous posets
Theoretical Computer Science
Duality beyond sober spaces: topological spaces and observation frames
Selected papers of the workshop on Topology and completion in semantics
Toward an infinitary logic of domains: Abramsky logic for transition systems
Information and Computation
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Modal logic
Theoretical Computer Science - Selected papers of CMCS'03
A coalgebraic view on positive modal logic
Theoretical Computer Science - Selected papers of CMCS'03
A domain equation for bisimulation
Information and Computation
ACM SIGACT News
Coalgebraic Modal Logic Beyond Sets
Electronic Notes in Theoretical Computer Science (ENTCS)
Functorial Coalgebraic Logic: The Case of Many-sorted Varieties
Electronic Notes in Theoretical Computer Science (ENTCS)
Bialgebraic methods and modal logic in structural operational semantics
Information and Computation
Free modal algebras: a coalgebraic perspective
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
The goldblatt-thomason theorem for coalgebras
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
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
Coalgebraic logic and synthesis of mealy machines
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Structural Operational Semantics and Modal Logic, Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Presenting functors on many-sorted varieties and applications
Information and Computation
On monotone modalities and adjointness
Mathematical Structures 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
Ultrafilter extensions for coalgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Testing semantics: connecting processes and process logics
AMAST'06 Proceedings of the 11th international conference on Algebraic Methodology and Software Technology
The duality of state and observation in probabilistic transition systems
TbiLLC'11 Proceedings of the 9th international conference on Logic, Language, and Computation
Stone Duality for Markov Processes
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
Duality in Logic and Computation
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category χ. The propositional logic used to reason about state spaces from χ is modelled by the Stone dual ${\mathcal A}$ of χ (e.g. if χ is Stone spaces then ${\mathcal A}$ is Boolean algebras and the propositional logic is the classical one). In order to obtain a modal logic for transition systems (i.e. for T-coalgebras) we consider the functor L on ${\mathcal A}$ that is dual to T. An adequate modal logic for T-coalgebras is then obtained from the category of L-algebras which is, by construction, dual to the category of T-coalgebras. The logical meaning of the duality is that the logic is sound and complete and expressive (or fully abstract) in the sense that non-bisimilar states are distinguished by some formula. We apply the framework to Vietoris coalgebras on topological spaces, using the duality between spaces and observation frames, to obtain adequate logics for transition systems on posets, sets, spectral spaces and Stone spaces.