Year: 2023
Type: article
Abstract: This article revisits soundness and completeness of proof systems for proving that sets of states in infinite-state labeled transition systems satisfy formulas in the modal mu-calculus in order to develop proof techniques that permit the seamless inclusion of new features in this logic. Our approach relies on novel results in lattice theory, which give constructive characterizations of both greatest and least fixpoints of monotonic functions over complete lattices. We show how these results may be used to reason about the sound and complete tableau method for this problem due to Bradfield and Stirling. We also show how the flexibility of our lattice-theoretic basis simplifies reasoning about tableau-based proof strategies for alternative classes of systems. In particular, we extend the modal mu-calculus with timed modalities, and prove that the resulting tableau method is sound and complete for timed transition systems.
DOI: 10.1145/3622786
Authors: Rance Cleaveland, Jeroen J. A. Keiren
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4386711086