Semantical cut-elimination for the provability logic of true arithmetic
Logic
2023-09-13 v1
Abstract
The quasi-normal modal logic GLS is a provability logic formalizing the arithmetical truth. Kushida (2020) gave a sequent calculus for GLS and proved the cut-elimination theorem. This paper introduces semantical characterizations of GLS and gives a semantical proof of the cut-elimination theorem. These characterizations can be generalized to other quasi-normal modal logics.
Keywords
Cite
@article{arxiv.2309.05948,
title = {Semantical cut-elimination for the provability logic of true arithmetic},
author = {Ryo Kashima and Yutaka Kato},
journal= {arXiv preprint arXiv:2309.05948},
year = {2023}
}