{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6R7BM4UKWCCXBCIMSZX6OLFLT7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e791cf62b5e272a17c46a265e3503ec64dd7e8ab31c86c7af0fe7257a83d6b52","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"cs.LO","submitted_at":"2007-06-27T15:15:57Z","title_canon_sha256":"13339fd05f4d0e09490a00cff59f42eb52c1810ba18c51d4de1e0222efc82c59"},"schema_version":"1.0","source":{"id":"0706.4044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.4044","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"0706.4044v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.4044","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"6R7BM4UKWCCX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6R7BM4UKWCCXBCIM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6R7BM4UK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:721b10df302de4da92cf0fa91e358d7d01c9b129a69fb0050341e5e93fced171","target":"graph","created_at":"2026-05-18T04:31:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank-1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACE-bounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generi","authors_text":"Dirk Pattinson, Lutz Schr\\\"oder","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"cs.LO","submitted_at":"2007-06-27T15:15:57Z","title":"PSPACE Bounds for Rank-1 Modal Logics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4044","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:028e0584f74ef07033a6d185a51115872fe7b6d3b9e0ea58270cad7236aaabf4","target":"record","created_at":"2026-05-18T04:31:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e791cf62b5e272a17c46a265e3503ec64dd7e8ab31c86c7af0fe7257a83d6b52","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"cs.LO","submitted_at":"2007-06-27T15:15:57Z","title_canon_sha256":"13339fd05f4d0e09490a00cff59f42eb52c1810ba18c51d4de1e0222efc82c59"},"schema_version":"1.0","source":{"id":"0706.4044","kind":"arxiv","version":1}},"canonical_sha256":"f47e16728ab08570890c966fe72cab9fdf77cb282c83db11d0d4ab8635642b45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47e16728ab08570890c966fe72cab9fdf77cb282c83db11d0d4ab8635642b45","first_computed_at":"2026-05-18T04:31:31.514386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.514386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tkQAL2Xcd5kRsEHWDxXsGwWvAwZb3LOrjRWr/lA3dBiQXQfFRrxDc2g7DErkAD6HDsqmpGaOvDlJyM5uz3NlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.514838Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.4044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:028e0584f74ef07033a6d185a51115872fe7b6d3b9e0ea58270cad7236aaabf4","sha256:721b10df302de4da92cf0fa91e358d7d01c9b129a69fb0050341e5e93fced171"],"state_sha256":"594261e4b55d521e823964f9218187256d8220b05d888c5ccb3fa701f33aaae7"}