The Topological Mu-Calculus: completeness and decidability

2021/05/18 by Alexandru Baltag, Baltag, Alexandru, Nick Bezhanishvili +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2105.08231

openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 T₀ 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.

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