Logics Containing wK4: Selection à la Fine
Logic in Computer Science
2026-06-30 v1
Abstract
We generalize Fine's Iterative Selection Method to the weakly transitive setting. In particular, this provides a transparent frame-theoretic proof of the finite model property for (strongly) cofinal subframe logics extending wK4, which was previously established using algebraic methods. Using the same construction, we generalize Fine's Finite Width Theorem to the weakly transitive setting, connecting these two celebrated theorems of Fine.
Cite
@article{arxiv.2606.31920,
title = {Logics Containing wK4: Selection à la Fine},
author = {Simon Santschi and Niels C. Vooijs},
journal= {arXiv preprint arXiv:2606.31920},
year = {2026}
}
Comments
In Proceedings AiML 2026, arXiv:2606.29444