Beyond the class of locally finite height Kripke models for provability logic

The paper [K. Sasaki & Y. Tanaka 2024: An $\omega$-rule for the logic of provability and its models, Studia Logica 112] presents the propositional logic NGL, an extension of the provability logic GL with an infinitary inference rule, and proves simple completeness theorem w.r.t. the class LF of locally finite height Kripke models. We provide a strongly complete modification of NGL and a family of Barwise-complete infinitary logics that correspond to specific subclasses of the class of all conversely well-founded strict posets that are proper superclasses of LF.
The talk is based on joint work with Zoran Ognjanović and Aleksandar Perović.