{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:63HLA2XB3IPBPGCCRYNMJG5CLE","short_pith_number":"pith:63HLA2XB","schema_version":"1.0","canonical_sha256":"f6ceb06ae1da1e1798428e1ac49ba2590fac0d92f50f0fff93cfa0249dc2adf8","source":{"kind":"arxiv","id":"1209.2620","version":1},"attestation_state":"computed","paper":{"title":"Probabilities on Sentences in an Expressive Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.LO","math.PR"],"primary_cat":"cs.LO","authors_text":"John W. Lloyd, Kee Siong Ng, Marcus Hutter, William T. B. Uther","submitted_at":"2012-09-12T14:17:09Z","abstract_excerpt":"Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.2620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-09-12T14:17:09Z","cross_cats_sorted":["cs.AI","cs.LG","math.LO","math.PR"],"title_canon_sha256":"7da426ad7110342c5486662fc2ceb7a2f06bafa9a5c2cba584e667da9708662c","abstract_canon_sha256":"36c78b408ef515f28d76b84622b8ddcd6c0e349d54ab8b734cd9a1b08c698b96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:42.630307Z","signature_b64":"dtdodmBGueJsXouvZIJsJb3dUlaE0I4xIkUMlss1a2SrCXJx1By8sJJKDpazI1zvmmQ7ynBh9L//pAOT9WQWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ceb06ae1da1e1798428e1ac49ba2590fac0d92f50f0fff93cfa0249dc2adf8","last_reissued_at":"2026-05-18T03:45:42.629569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:42.629569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilities on Sentences in an Expressive Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","math.LO","math.PR"],"primary_cat":"cs.LO","authors_text":"John W. Lloyd, Kee Siong Ng, Marcus Hutter, William T. B. Uther","submitted_at":"2012-09-12T14:17:09Z","abstract_excerpt":"Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2620","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.2620","created_at":"2026-05-18T03:45:42.629686+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.2620v1","created_at":"2026-05-18T03:45:42.629686+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2620","created_at":"2026-05-18T03:45:42.629686+00:00"},{"alias_kind":"pith_short_12","alias_value":"63HLA2XB3IPB","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"63HLA2XB3IPBPGCC","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"63HLA2XB","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE","json":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE.json","graph_json":"https://pith.science/api/pith-number/63HLA2XB3IPBPGCCRYNMJG5CLE/graph.json","events_json":"https://pith.science/api/pith-number/63HLA2XB3IPBPGCCRYNMJG5CLE/events.json","paper":"https://pith.science/paper/63HLA2XB"},"agent_actions":{"view_html":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE","download_json":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE.json","view_paper":"https://pith.science/paper/63HLA2XB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.2620&json=true","fetch_graph":"https://pith.science/api/pith-number/63HLA2XB3IPBPGCCRYNMJG5CLE/graph.json","fetch_events":"https://pith.science/api/pith-number/63HLA2XB3IPBPGCCRYNMJG5CLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE/action/storage_attestation","attest_author":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE/action/author_attestation","sign_citation":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE/action/citation_signature","submit_replication":"https://pith.science/pith/63HLA2XB3IPBPGCCRYNMJG5CLE/action/replication_record"}},"created_at":"2026-05-18T03:45:42.629686+00:00","updated_at":"2026-05-18T03:45:42.629686+00:00"}