Semantical cut-elimination for the provability logic of true arithmetic

Ryo Kashima, Yutaka Kato

Published 2023-09-12Version 1

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.