Algebraic laws for nondeterminism and concurrency
Journal of the ACM (JACM)
Additions and corrections to “Terminal coalgebras in well-founded set theory”
Theoretical Computer Science
Objects and classes, co-algebraically
Object orientation with parallelism and persistence
A small final coalgebra theorem
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
From modal logic to terminal coalgebras
Theoretical Computer Science
What is the coalgebraic analogue of Birkhoff's variety theorem?
Theoretical Computer Science
Category Theory and Computer Science
On Observing Nondeterminism and Concurrency
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Exercises in coalgebraic specification
Algebraic and coalgebraic methods in the mathematics of program construction
Theoretical Computer Science - Selected papers of CMCS'03
ACM SIGACT News
The goldblatt-thomason theorem for coalgebras
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
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An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets. The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor. The states of this final coalgebra are certain "maximal" sets of formulas that have natural syntactic closure properties.The syntax of these logics extends that of previously developed modal languages for polynomial coalgebras by adding formulas that express the "termination" of certain functions induced by transition paths. A completeness theorem is proven for the logic of functors which have the Lindenbaum property that every consistent set of formulas has a maximal extension. This property is shown to hold if the deducibility relation is generated by countably many inference rules.A counter-example to completeness is also given. This is a polynomial functor that is not Lindenbaum: it has an uncountable set of formulas that is deductively consistent but has no maximal extension and is unsatisfiable, even though all of its countable subsets are satisfiable.