Establish syntactic cut-elimination for the LTL linear nested sequent calculus

Establish a syntactic cut-elimination theorem for the non-wellfounded and cyclic linear nested sequent calculi for linear temporal logic, using the additional structural expressiveness of linear nested sequents to address the unresolved cut-elimination problem known for existing non-wellfounded Gentzen calculi for LTL.

Background

Existing non-wellfounded Gentzen calculi for LTL, including the systems cited by Brünnler and Lange, Kokkinis and Studer, and Alonderis et al., do not have known syntactic cut-elimination proofs. The paper proposes linear nested sequents as a richer structural formalism that might make such a proof possible, but it does not establish cut-elimination for its own systems.

The passage explicitly combines the unresolved status of cut-elimination for the existing Gentzen calculi with the authors’ conjecture that linear nested sequents provide a pathway toward resolving it. This is a concrete open proof-theoretic problem rather than a general future-work aspiration.

References

First, syntactic cut-elimination remains open for all existing non-wellfounded Gentzen calculi for $LTL$, and we conjecture that the additional structural expressiveness of linear nested sequents provides a pathway to resolving this problem.

— Non-Wellfounded and Cyclic Proofs for LTL: A Syntactic Correspondence with Linear Nested Sequents  (2610.18798 - Lyon et al., 13 Oct 2026) in Section 1, “LTL and Related Systems”