2016/09/13 by Nick Bezhanishvili, Clemens Kupke
Computer Science · #Algebra over a field #Fixed point #Fixed-point theorem #Formal Methods in Verification #Graph #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Modal μ-calculus #Monotone polygon #Topology (electrical circuits) #cs.GT #cs.LO
paper · pdf · doi:10.4204/eptcs.226.4
published as EPTCS 226, 2016, pp. 46-60 · In Proceedings GandALF 2016, arXiv:1609.03648
openalex publication_date 2016/09/13 · arxiv created 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2016/09/23 · openalex updated_date 2026/08/06
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.