### Abstract

We extend our approach for verifying properties of graph transformation systems using suitable abstractions. In the original approach properties are specified as formulae of a propositional temporal logic whose atomic predicates are monadic second-order graph formulae. We generalize this aspect by considering more expressive logics, where edge quantifiers and temporal modalities can be interleaved, a feature which allows, e.g., to trace the history of objects in time. This requires the use of graph transition systems, a generalization of transition systems where states and transitions are mapped to graphs and graph morphisms, respectively, and of a corresponding notion of abstraction. After characterizing fragments of the logic which can be safely checked on the approximations, we show how the verification of the logic over graph transformation systems can be reduced to the verification of a logic over suitably defined Petri nets.

Original language | English |
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Title of host publication | Recent Trends in Algebraic Development Techniques : 18th International Workshop, WADT 2006, La Roche en Ardenne, Belgium, June 1-3, 2006, Revised Selected Papers |

Publisher | Springer Berlin Heidelberg |

Publication date | 2007 |

Pages | 1-20 |

ISBN (Print) | 978-3-540-71997-7 |

ISBN (Electronic) | 978-3-540-71998-4 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

Event | 18th International Workshop on Algebraic Development Techniques - La Roche en Ardenne, Belgium Duration: 1 Jun 2006 → 3 Jun 2006 Conference number: 18 |

### Conference

Conference | 18th International Workshop on Algebraic Development Techniques |
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Number | 18 |

Country | Belgium |

City | La Roche en Ardenne |

Period | 01/06/2006 → 03/06/2006 |

Series | Lecture Notes in Computer Science |
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Volume | 4409 |

ISSN | 0302-9743 |

## Cite this

Baldan, P., Corradini, A., König, B., & Lluch Lafuente, A. (2007). A Temporal Graph Logic for Abstractions of Graph Rewriting Systems. In

*Recent Trends in Algebraic Development Techniques: 18th International Workshop, WADT 2006, La Roche en Ardenne, Belgium, June 1-3, 2006, Revised Selected Papers*(pp. 1-20). Springer Berlin Heidelberg. Lecture Notes in Computer Science, Vol.. 4409 https://doi.org/10.1007/978-3-540-71998-4_1