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Bi-modal G¨ odel logic over [0, 1]-valued Kripke frames.Journal of Logic and Computation, 25(1):37–55, 2015","work_id":"01b7c30a-141a-4feb-8bef-e3d97e2f0be0","year":2015}],"snapshot_sha256":"e6b5e1b7254f45fc5e27a503982e353000373764ef475d74124425772ec8a6e5"},"source":{"id":"2605.15810","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T19:46:42.267359Z","id":"7f50c853-b48a-4d32-9382-34284b7f6e19","model_set":{"reader":"grok-4.3"},"one_line_summary":"Resolves open problem by proving natural extensions of modal Gödel logics are incomplete for finite models and supplies new complete axiomatizations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Natural axiomatic extensions fail to restore completeness for modal Gödel logics over finite Gödel-Kripke models.","strongest_claim":"The natural candidate axiomatic extensions do not restore completeness with respect to finite Gödel-Kripke models, thereby resolving a 15 year open problem. 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