The Topological Mu-Calculus: completeness and decidability

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 TD 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.