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arXiv · 2511.01428

Uniform interpolation for interpretability logic

Sebastijan Horvat·Borja Sierra Miranda·Thomas Studer
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Abstract

We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In addition, we show that the non-wellfounded proof theory of IL is well-behaved, i.e., that cyclic proofs suffice. This makes it possible to prove uniform interpolation for IL. As a corollary we also provide a proof of uniform interpolation for the interpretability logic ILP.

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Sebastijan Horvat, Borja Sierra Miranda, Thomas Studer. 2025-11-03. Uniform interpolation for interpretability logic. https://arxiv.org/abs/2511.01428

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