On a Dynamic Logic for Graph Rewriting

Mathias Winckel (1) , Ralph Matthes (1, 2)

1 IRIT-ACADIE - Assistance à la Certification d’Applications DIstribuées et Embarquées
2 CNRS - Centre National de la Recherche Scientifique

Initially introduced by P. Balbiani, R. Echahed and A.Herzig, this dynamic logic is useful to talk about properties on termgraphs and to characterize transformations on these graphs. Also are presented the deterministic labelled graphs for which the logical framework 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 representation 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 characterization of graph rewriting, which was the initial purpose.

Mots clés: Dynamic logic; Graph rewriting; Adequation issues

Domaines: Génie logiciel [cs.SE]; Systèmes embarqués; Cryptographie et sécurité [cs.CR]; Interface homme-machine [cs.HC]; Architectures Matérielles [cs.AR]; Modélisation et simulation

Mathias Winckel, Ralph Matthes. On a Dynamic Logic for Graph Rewriting. 2nd International Workshop on Algebraic, Logical, and Algorithmic Methods of System Modeling, Specification and Verification (SMSV 2013), Jan 2013, Kherson, Ukraine. pp. 506-520. ⟨hal-01233230⟩