## Abstract

We define a new logic-induced notion of bisimulation (called ρ-bisimulation) for coal-

gebraic modal logics given by a logical connection, and investigate its properties. We

show that it is structural in the sense that it is defined only in terms of the coalge-

bra structure and the one-step modal semantics and, moreover, can be characterised

by a form of relation lifting. Furthermore we compare ρ-bisimulations to several

well-known equivalence notions, and we prove that the collection of bisimulations

between two models often forms a complete lattice. The main technical result is a

Hennessy-Milner type theorem which states that, under certain conditions, logical

equivalence implies ρ-bisimilarity. In particular, the latter does not rely on a duality

between functors T (the type of the coalgebras) and L (which gives the logic), nor on

properties of the logical connection ρ.

gebraic modal logics given by a logical connection, and investigate its properties. We

show that it is structural in the sense that it is defined only in terms of the coalge-

bra structure and the one-step modal semantics and, moreover, can be characterised

by a form of relation lifting. Furthermore we compare ρ-bisimulations to several

well-known equivalence notions, and we prove that the collection of bisimulations

between two models often forms a complete lattice. The main technical result is a

Hennessy-Milner type theorem which states that, under certain conditions, logical

equivalence implies ρ-bisimilarity. In particular, the latter does not rely on a duality

between functors T (the type of the coalgebras) and L (which gives the logic), nor on

properties of the logical connection ρ.

Original language | English |
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Title of host publication | Advances in Modal Logic |

Editors | Nicola Olivetti, Rineke Verbrugge, Sara Negri, Gabriel Sandu |

Publisher | College Publications |

Pages | 289-308 |

Volume | 13 |

ISBN (Print) | 978-1-84890-341-8 |

Publication status | Published - 2020 |

Externally published | Yes |

Event | Advances in Modal Logic 2020 - University of Helsinki, Helsinki, Finland Duration: 24-Aug-2020 → 28-Aug-2020 https://www2.helsinki.fi/en/conferences/advances-in-modal-logic-2020 |

### Conference

Conference | Advances in Modal Logic 2020 |
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Abbreviated title | AiML |

Country/Territory | Finland |

City | Helsinki |

Period | 24/08/2020 → 28/08/2020 |

Internet address |