Uniform interpolation for interpretability logic
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911247377629184 |
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| author | Horvat, Sebastijan Miranda, Borja Sierra Studer, Thomas |
| author_facet | Horvat, Sebastijan Miranda, Borja Sierra Studer, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform interpolation for interpretability logic Horvat, Sebastijan Miranda, Borja Sierra Studer, Thomas Logic 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. |
| title | Uniform interpolation for interpretability logic |
| topic | Logic |
| url | https://arxiv.org/abs/2511.01428 |