The Topological Mu-Calculus: completeness and decidability

05/18/2021

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by   Alexandru Baltag, et al.

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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 model-theoretic, 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.