Bezhanishvili, Nick and Kupke, Clemens (2016) Games for topological fixpoint logic. In: Proceedings of the Seventh International Symposium on Games, Automata, Logics, and Formal Verification. Electronic Proceedings in Theoretical Computer Science, pp. 1-15.
Bezhanishvili_Kupke_GandALF_2016_games_for_topological_fixpoint_logic.pdf - Accepted Author Manuscript
Download (243kB) | Preview
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.
|Item type:||Book Section|
|Keywords:||modal logic, topology, modal fixpoint logic, graph games, Mathematics, Geometry and Topology, Logic|
|Subjects:||Science > Mathematics|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||30 Sep 2016 12:52|
|Last modified:||25 Apr 2017 01:04|