{"paper":{"title":"A proof system for the positive fragment of GL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yoshihito Tanaka","submitted_at":"2026-05-19T04:37:26Z","abstract_excerpt":"In this paper, we present a proof system $\\mathsf{GL}_{+}^{\\top\\bot}$, which is based on a sequent system $\\mathsf{K}_{+}^{\\top\\bot}$ given by Dunn, for the positive fragment of $\\mathsf{GL}$. Positive modal formulas are modal formulas that contain neither negation symbols nor implication symbols. More precisely, they are modal formulas constructed from the connectives $\\lor$, $\\land$, $\\Diamond$, $\\Box$, $\\bot$, $\\top$, and propositional variables. The logic $\\mathsf{GL}$ is the least normal modal logic that contains $\\mathsf{K}$ and the L\\\"{o}b formula $\\Box(\\Box p\\supset p)\\supset\\Box p$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19349","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/2605.19349/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"}