{"paper":{"title":"Interpolation via Generalized Splitting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Lutz Stra{\\ss}burger","submitted_at":"2026-07-26T18:50:09Z","abstract_excerpt":"We propose a new proof theoretical method for proving Lyndon interpolation. Our proof does not use the sequent calculus but is based on a generalization of the splitting lemma in deep inference. We then formulate the interpolation theorem as a decomposition of a derivation into an up-fragment and a down-fragment. This can be seen as (i) a strengthening of the standard formulation of the interpolation theorem, and (ii) a generalization of the cut elimination theorem. We demonstrate the flexibility of our approach by applying it to linear logic, classical logic, and modal logics. For this, we al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23798","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23798/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}