A Logic of Coequations

  • Jiri Adámek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3634)


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.


Logical Consequence Inference Rule Free Algebra Small Cardinal Unique Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jiri Adámek
    • 1
  1. 1.Institute of Theoretical Computer ScienceTechnical UniversityBraunschweigGermany

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