On a Dynamic Logic for Graph Rewriting
Mathias Winckel, Ralph Matthes · 2013
Initially introduced by P. Balbiani, R. Echahed and A. Herzig, this dynamic logic is useful to talk about properties on ter- mgraphs and to characterize transformations on these graphs. Also are presented the deterministic labelled graphs for which the logical frame- work is designed. This logic has been the starting point of a formal development, using the Coq proof assistant, to design a logical and algorithmic framework useful for verifyin and proving graph rewriting. The formalization allowed us to figure out some ambiguities in the involved concepts. This formalization is not the topic here but the clear view brought to us by the formal work, so the results will be expressed using the original mathematical objects of this logic. Some problems of this logic are demonstrated, relatively to the repre- sentation of graph rewriting. Some are minor issues but some are far more important for the adequation between the formulas about graph rewriting and the actual rewriting systems. Invalidating some resulting propositions, solutions are given to reestablish the logical characteriza- tion of graph rewriting, which was the initial purpose.