Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Modal operators and the formal dual of Birkhoff's completeness theorem
Mathematical Structures in Computer Science
The temporal logic of coalgebras via Galois algebras
Mathematical Structures in Computer Science
On tree coalgebras and coalgebra presentations
Theoretical Computer Science
Theoretical Computer Science - Logic, semantics and theory of programming
On the final sequence of a finitary set functor
Theoretical Computer Science
Coequational Logic for Finitary Functors
Electronic Notes in Theoretical Computer Science (ENTCS)
Characterising behavioural equivalence: three sides of one coin
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Coequational logic for accessible functors
Information and Computation
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By Rutten's dualization of the Birkhoff Variety Theorem, a collection of coalgebras is a covariety (i.e., is closed under coproducts, subcoalgebras, and quotients) iff it can be presented by a subset of a cofree coalgebra. We introduce inference rules for these subsets, and prove that they are sound and complete. For example, given a polynomial endofunctor of a signature Σ, the cofree coalgebra consists of colored Σ-trees, and we prove that a set T of colored trees is a logical consequence of a set S iff T contains every tree such that all recolorings of all its subtrees lie in S. Finally, we characterize covarieties whose presentation needs only n colors.