A Logic on Subobjects and Recognizability

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.

• Type: Journal
• Year: 2010
• Where: IFIPTCS
• Authors: Harrie Jan Sander Bruggink, Barbara König
• Keywords: IFIPTCS 2010, Logic, Monadic Graph Logic, So-called Automaton Functors, Theoretical Computer Science