### Abstract

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of.

Original language | English |
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Title of host publication | Graph Transformations : 5th International Conference, ICGT 2010, Enschede, The Netherlands, September 27–October 2, 2010. Proceedings |

Publisher | Springer Berlin Heidelberg |

Publication date | 2010 |

Pages | 282-297 |

ISBN (Print) | 978-3-642-15927-5 |

ISBN (Electronic) | 978-3-642-15928-2 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 5th International Conference on Graph Transformation - Enschede, Netherlands Duration: 27 Sep 2010 → 2 Oct 2010 |

### Conference

Conference | 5th International Conference on Graph Transformation |
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Country | Netherlands |

City | Enschede |

Period | 27/09/2010 → 02/10/2010 |

Series | Lecture Notes in Computer Science |
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Volume | 6372 |

ISSN | 0302-9743 |

## Cite this

Gadducci, F., Lluch Lafuente, A., & Vandin, A. (2010). Counterpart semantics for a secondorder mu-calculus. In

*Graph Transformations: 5th International Conference, ICGT 2010, Enschede, The Netherlands, September 27–October 2, 2010. Proceedings*(pp. 282-297). Springer Berlin Heidelberg. Lecture Notes in Computer Science, Vol.. 6372 https://doi.org/10.1007/978-3-642-15928-2_19