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arXiv · 2105.08231

The Topological Mu-Calculus: completeness and decidability

Alexandru Baltag·Nick Bezhanishvili·David Fernández-Duque
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Abstract

We study the topological $\mu$-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 $\mu$-calculus, providing general completeness results for all natural fragments of $\mu$-calculus over many different classes of relational frames. Unlike most other such proofs for $\mu$-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.

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Alexandru Baltag, Nick Bezhanishvili, David Fernández-Duque. 2021-05-18. The Topological Mu-Calculus: completeness and decidability. https://arxiv.org/abs/2105.08231

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