Uniform Interpolation
Logic
2026-02-11 v2 Logic in Computer Science
Abstract
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic propositional logic. We outline how this theorem may be proved semantically via the definability of bisimulation quantifiers, and how it generalizes to an open mapping theorem between Esakia spaces. We also discuss connections between uniform interpolation and research in categorical logic, algebra, and model theory.
Cite
@article{arxiv.2512.15391,
title = {Uniform Interpolation},
author = {Sam van Gool},
journal= {arXiv preprint arXiv:2512.15391},
year = {2026}
}
Comments
To appear as chapter 9 in: B. ten Cate, J. C. Jung, P. Koopmann, C. Wernhard, F. Wolter (eds), Theory and Applications of Craig Interpolation. Ubiquity Press (2026)