English

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.

Keywords

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