The Topological Mu-Calculus: completeness and decidability

We study the topological µ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over T 0 and T D spaces. We also investigate relational µ-calculus, providing general completeness results for all natur...

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Veröffentlicht in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 13
Hauptverfasser: Baltag, Alexandru, Bezhanishvili, Nick, Fernandez-Duque, David
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 29.06.2021
Schlagworte:
Computational modeling
Computer science
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Zusammenfassung:We study the topological µ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over T 0 and T D spaces. We also investigate relational µ-calculus, providing general completeness results for all natural fragments of µ-calculus over many different classes of relational frames. Unlike most other such proofs for µ-calculus, ours is modeltheoretic, making an innovative use of a known Modal Logic method (-the 'final' submodel of the canonical model), that has the twin advantages of great generality and essential simplicity.
DOI:10.1109/LICS52264.2021.9470560