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A Logic on Subobjects and Recognizability

  • H. J. Sander Bruggink
  • Barbara König
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 323)

Abstract

We introduce a simple logic that allows to quantify over the subobjects of a categorical object. We subsequently show that, for the category of graphs, this logic is equally expressive as second-order monadic graph logic (msogl). Furthermore we show that for the more general setting of hereditary pushout categories, a class of categories closely related to adhesive categories, we can recover Courcelle’s result that every msogl-expressible property is recognizable. This is done by giving an inductive translation of formulas of our logic into so-called automaton functors which accept recognizable languages of cospans.

Keywords

Atomic Formula Tree Automaton Categorical Logic Typing Morphism Category Graph 
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

© IFIP 2010

Authors and Affiliations

  • H. J. Sander Bruggink
    • 1
  • Barbara König
    • 1
  1. 1.Universität Duisburg-EssenGermany

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