{"paper":{"title":"A Proof-Theoretic Study of Modal Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Hirohiko Kushida","submitted_at":"2026-05-18T08:34:48Z","abstract_excerpt":"This paper proposes a basic proof theoretic framework for major modal logics: {\\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\\sf K} and its standard extensions with combinations of axioms: $T, D, 4, B, 5$. First we propose a reasonable explanation of how the standard sequent and hypersequent calculi for some of those modal logics such as {\\sf K, T, D, S4, S5} emerge on the basis of the framework. Then, by a syntactic method, we prove the cut-elimination theorem for the modal logics ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18043","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/2605.18043/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:59.302734Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.494160Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3f1dad8ff568be0af04a86c47954180336f8cd24b98cf406ada305a3189c86f4"},"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"}