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Abstract
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.
Original language | English |
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Title of host publication | Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification |
Editors | Domenico Cantone, Giorgio Delzanno |
Pages | 46-60 |
Number of pages | 15 |
Publication status | Published - 13 Sept 2016 |
Event | Seventh International Symposium on Games, Automata, Logics, and Formal Verification - University of Catania, Catania, Italy Duration: 14 Sept 2016 → 16 Sept 2016 Conference number: 7 |
Conference
Conference | Seventh International Symposium on Games, Automata, Logics, and Formal Verification |
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Abbreviated title | GandALF |
Country/Territory | Italy |
City | Catania |
Period | 14/09/16 → 16/09/16 |
Keywords
- modal logic
- topology
- modal fixpoint logic
- graph games
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Projects
- 1 Finished
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Coalgebraic Foundations of Semi-Structured Data (EPSRC First Grant)
Kupke, C. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/02/16 → 31/01/18
Project: Research