arXiv Analytics

Sign in

arXiv:2307.06846 [math.LO]AbstractReferencesReviewsResources

A note on the incompleteness of Afshari & Leigh's system Clo

Johannes Kloibhofer

Published 2023-07-13Version 1

The system $\mathsf{Clo}$ is a cyclic, cut-free proof system for the modal $\mu$-calculus. It was introduced by Afshari & Leigh as an intermediate system in their intent to show the completeness of Kozen's axiomatisation for the modal $\mu$-calculus. We prove that $\mathsf{Clo}$ is incomplete by giving a valid sequent that is not provable in $\mathsf{Clo}$.

Categories: math.LO
Related articles: Most relevant | Search more
arXiv:1802.10261 [math.LO] (Published 2018-02-28)
A cut-free proof system for a predicate extension of the logic of provability
arXiv:math/0408144 [math.LO] (Published 2004-08-11, updated 2004-11-15)
Is Complexity a Source of Incompleteness?
arXiv:1805.08209 [math.LO] (Published 2018-05-20)
Possible Worlds, Incompleteness and Undefinability

Links

Toolbox