The Topological Mu-Calculus: Completeness and Decidability

IF 2.3 2区计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE

Journal of the ACM Pub Date : 2023-09-07 DOI:10.1145/3623268

A. Baltag, N. Bezhanishvili, David Fernández-Duque

引用次数: 0

Abstract

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 TD 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.

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拓扑mu微积分:完备性和可判定性

我们研究了基于Cantor导数和闭模的拓扑μ微积分，证明了一般拓扑空间以及T0和TD空间上的完备性、可判决性和有限模型性质。我们还研究了关系μ-演算，给出了在许多不同类型的关系框架上μ-演算的所有自然片段的一般完备性结果。与大多数其他此类μ-演算的证明不同，我们的证明是模型论的，创新地使用了模态逻辑(规范模型的“最终”子模型)的已知方法，这种方法具有很强的通用性和本质上的简单性的双重优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the ACM 工程技术-计算机：理论方法

CiteScore

7.50

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The best indicator of the scope of the journal is provided by the areas covered by its Editorial Board. These areas change from time to time, as the field evolves. The following areas are currently covered by a member of the Editorial Board: Algorithms and Combinatorial Optimization; Algorithms and Data Structures; Algorithms, Combinatorial Optimization, and Games; Artificial Intelligence; Complexity Theory; Computational Biology; Computational Geometry; Computer Graphics and Computer Vision; Computer-Aided Verification; Cryptography and Security; Cyber-Physical, Embedded, and Real-Time Systems; Database Systems and Theory; Distributed Computing; Economics and Computation; Information Theory; Logic and Computation; Logic, Algorithms, and Complexity; Machine Learning and Computational Learning Theory; Networking; Parallel Computing and Architecture; Programming Languages; Quantum Computing; Randomized Algorithms and Probabilistic Analysis of Algorithms; Scientific Computing and High Performance Computing; Software Engineering; Web Algorithms and Data Mining