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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Bibliographic Details
Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 13
Main Authors: Baltag, Alexandru, Bezhanishvili, Nick, Fernandez-Duque, David
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Computational modeling
Computer science
Online Access:Get full text
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Summary: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