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arXiv · 2602.16318

Interpolation in Proof Theory

Iris van der Giessen·Raheleh Jalali·Roman Kuznets
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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.

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Iris van der Giessen, Raheleh Jalali, Roman Kuznets. 2026-02-18. Interpolation in Proof Theory. https://arxiv.org/abs/2602.16318

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