We study the topological μ-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability, and finite model property over general topological spaces, as well as over T₀ and T_D spaces. We also investigate the relational μ-calculus, providing general completeness results for all natural fragments of the μ-calculus over many different classes of relational frames. Unlike most other such proofs for μ-calculi, ours is model theoretic, making an innovative use of a known method from modal logic (the ‘final’ submodel of the canonical model), which has the twin advantages of great generality and essential simplicity.

我们基于康托导数和闭包模态研究拓扑 μ 演算，证明一般拓扑空间以及 T 0 和 T D 空间上的完整性、可判定性_和有限模型_属性。我们还研究了关系 μ 演算，为许多不同类别的关系框架上的 μ 演算的所有自然片段提供了一般完整性结果。与大多数其他此类 μ 演算的证明不同，我们的证明是模型理论，创新地使用了模态逻辑（规范模型的“最终”子模型）中的已知方法，具有高度通用性和本质简单性的双重优点。