Interpolation in Proof Theory
Abstract
This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion are two foundational techniques: Maehara's method for Craig interpolation and Pitts' method for uniform interpolation. The chapter demonstrates how these methods lead to results on the existence of well-behaved proof systems in the contemporary framework of universal proof theory and how they provide a road map for constructing interpolation proofs using modern proof formalisms. The emphasis of the chapter is on constructive, modular, and syntax-driven techniques that illuminate deeper connections between interpolation properties and proof systems.
Keywords
Cite
@article{arxiv.2602.16318,
title = {Interpolation in Proof Theory},
author = {Iris van der Giessen and Raheleh Jalali and Roman Kuznets},
journal= {arXiv preprint arXiv:2602.16318},
year = {2026}
}
Comments
The article will appear in Balder ten Cate, Jean Christoph Jung, Patrick Koopmann, Christoph Wernhard and Frank Wolter, editors. Theory and Applications of Craig Interpolation. Ubiquity Press, 2026