Abstract
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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Adámek, J. (2005). A Logic of Coequations. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_7
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DOI: https://doi.org/10.1007/11538363_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28231-0
Online ISBN: 978-3-540-31897-2
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