A. Baltag, N. Bezhanishvili, David Fernández-Duque
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The Topological Mu-Calculus: Completeness and Decidability
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.
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
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