{"paper":{"title":"Craig-Lyndon Interpolation for the Logic of Here and There with a Variation of Mints' Sequent System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A variation of Maehara's method constructs Craig-Lyndon interpolants for the logic of here and there using a modified Mints sequent system.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Christoph Wernhard","submitted_at":"2026-01-07T16:47:54Z","abstract_excerpt":"We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as G\\\"odel's $G_3$, a superintuitionistic logic of importance in logic programming. Our method adapts a recent interpolation technique that operates on classically encoded logic programs to a variation of Mints' sequent system for HT. The approach is characterized by two stages: First, a preliminary interpolant is constructed, a formula that is an interpolant in some sense but not yet the desired HT formula. In the second stage, an actual"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as Gödel's G3, a superintuitionistic logic of importance in logic programming.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the described variation of Mints' sequent system and the two-stage conversion process from preliminary to actual HT interpolant correctly yields valid Craig-Lyndon interpolants for arbitrary HT formulas.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A two-stage adaptation of Maehara's method using a modified Mints sequent system constructs Craig-Lyndon interpolants directly for HT logic formulas.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A variation of Maehara's method constructs Craig-Lyndon interpolants for the logic of here and there using a modified Mints sequent system.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"df6c7d88224db644182f1a5c26bd4e6386eb94364be177e9eb47b553ba27cb29"},"source":{"id":"2601.04080","kind":"arxiv","version":4},"verdict":{"id":"34dd7ab7-cdb2-47aa-91db-c134fd71defa","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T16:23:10.695848Z","strongest_claim":"We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as Gödel's G3, a superintuitionistic logic of importance in logic programming.","one_line_summary":"A two-stage adaptation of Maehara's method using a modified Mints sequent system constructs Craig-Lyndon interpolants directly for HT logic formulas.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the described variation of Mints' sequent system and the two-stage conversion process from preliminary to actual HT interpolant correctly yields valid Craig-Lyndon interpolants for arbitrary HT formulas.","pith_extraction_headline":"A variation of Maehara's method constructs Craig-Lyndon interpolants for the logic of here and there using a modified Mints sequent system."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.04080/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":1,"snapshot_sha256":"86028c96cb29f4c1000f2bca12977d8856494360c21325f2d69a29d48945db56"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}