2023/01/18 by Graham E. Leigh, Leigh, Graham E., Dominik Wehr +1 · 1 citation
Computer Science · #FOS: Mathematics #Formal Methods in Verification #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2301.07544
openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider cyclic proof systems in which derivations are graphs rather than trees. Such systems typically come with a condition that isolates which derivations are admitted as 'proofs', known as a the soundness condition. This soundness condition frequently takes the form of either a global trace condition, a property dependent on all infinite paths in the proof-graph, or a reset condition, a 'local' condition depending on the simple cycles only which, as a result, is typically stable under more proof transformations. In this article we present a general method for constructing cyclic proof systems with reset condition from cyclic proof with global trace conditions. In contrast to previous approaches, this method of generation is entirely independent of logic's semantics, only relying on combinatorial aspects of the notion of 'trace' and 'progress'. We apply this method to present reset proof systems for three cyclic proof systems from the literature: cyclic arithmetic, cyclic Gödel's T and cyclic tableaux for the modal μ-calculus.