### Abstract

Language | English |
---|---|

Title of host publication | Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification |

Editors | Domenico Cantone, Giorgio Delzanno |

Pages | 1-15 |

Number of pages | 15 |

Publication status | Published - 13 Sep 2016 |

Event | Seventh International Symposium on Games, Automata, Logics, and Formal Verification - University of Catania, Catania, Italy Duration: 14 Sep 2016 → 16 Sep 2016 Conference number: 7 |

### Conference

Conference | Seventh International Symposium on Games, Automata, Logics, and Formal Verification |
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Abbreviated title | GandALF |

Country | Italy |

City | Catania |

Period | 14/09/16 → 16/09/16 |

### Fingerprint

### Keywords

- modal logic
- topology
- modal fixpoint logic
- graph games

### Cite this

*Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification*(pp. 1-15)

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*Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification.*pp. 1-15, Seventh International Symposium on Games, Automata, Logics, and Formal Verification, Catania, Italy, 14/09/16.

**Games for topological fixpoint logic.** / Bezhanishvili, Nick; Kupke, Clemens.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Games for topological fixpoint logic

AU - Bezhanishvili, Nick

AU - Kupke, Clemens

PY - 2016/9/13

Y1 - 2016/9/13

N2 - Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we introduce games characterising clopen fixpoints of monotone operators on Stone spaces. These fixpoint games allow us to characterise the semantics for our topological fixpoint logic using a two-player graph game. Adequacy of this game is the main result of our paper. Finally, we define bisimulations for the topological structures under consideration and use our game semantics to prove that the truth of a formula of our topological fixpoint logic is bisimulation-invariant.

AB - Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we introduce games characterising clopen fixpoints of monotone operators on Stone spaces. These fixpoint games allow us to characterise the semantics for our topological fixpoint logic using a two-player graph game. Adequacy of this game is the main result of our paper. Finally, we define bisimulations for the topological structures under consideration and use our game semantics to prove that the truth of a formula of our topological fixpoint logic is bisimulation-invariant.

KW - modal logic

KW - topology

KW - modal fixpoint logic

KW - graph games

UR - http://gandalf2016.dmi.unict.it/

M3 - Conference contribution book

SP - 1

EP - 15

BT - Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification

A2 - Cantone, Domenico

A2 - Delzanno, Giorgio

ER -