A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic
Logic in Computer Science
2025-06-18 v1 Logic
Abstract
We present a labelled and non-wellfounded calculus for the bimodal provability logic CS. The system is obtained by modelling the Kripke-like semantics of this logic. As in arXiv:2309.00532, we enforce the second-order property of converse wellfoundedness by using techniques from cyclic proof theory. We will prove soundness and completeness of this system with respect to the semantics and provide a primitive decision procedure together with a way to extract countermodels.
Cite
@article{arxiv.2506.14307,
title = {A Non-Wellfounded and Labelled Sequent Calculus for Bimodal Provability Logic},
author = {Justus Becker},
journal= {arXiv preprint arXiv:2506.14307},
year = {2025}
}
Comments
Preprint, 15 pages