{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:F52U4HB2DVRE4WGHBPWJC7N7IF","short_pith_number":"pith:F52U4HB2","schema_version":"1.0","canonical_sha256":"2f754e1c3a1d624e58c70bec917dbf414f8d0c60b3cd779d7f7f1e52ad702045","source":{"kind":"arxiv","id":"1210.2620","version":3},"attestation_state":"computed","paper":{"title":"Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Am\\'elie Gheerbrant (School of Informatics, Balder ten Cate (Santa Cruz Department of Computer Science, University of California), University of Edinburgh)","submitted_at":"2012-10-09T14:51:25Z","abstract_excerpt":"We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., eac"},"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":"1210.2620","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2012-10-09T14:51:25Z","cross_cats_sorted":[],"title_canon_sha256":"979e1c8fbed24f1402173a7b6de3660c359eb86ae3679c3c62528d7e1ad12708","abstract_canon_sha256":"d184b065522711f5a6df61d8afbee557fd3a37d897b9984a7b6e98d10e308b25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:38.429907Z","signature_b64":"jOp+5P8XNKZvX9M3FvKmGdQoqmpjw74kWfvOsP/GVV5fM5dLGaFta1KZyIc+Rj1jgzH9XMYnOPOEoBhfiK6OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f754e1c3a1d624e58c70bec917dbf414f8d0c60b3cd779d7f7f1e52ad702045","last_reissued_at":"2026-05-18T01:37:38.429215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:38.429215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Am\\'elie Gheerbrant (School of Informatics, Balder ten Cate (Santa Cruz Department of Computer Science, University of California), University of Edinburgh)","submitted_at":"2012-10-09T14:51:25Z","abstract_excerpt":"We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., eac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2620","kind":"arxiv","version":3},"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":"1210.2620","created_at":"2026-05-18T01:37:38.429307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2620v3","created_at":"2026-05-18T01:37:38.429307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2620","created_at":"2026-05-18T01:37:38.429307+00:00"},{"alias_kind":"pith_short_12","alias_value":"F52U4HB2DVRE","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"F52U4HB2DVRE4WGH","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"F52U4HB2","created_at":"2026-05-18T12:27:04.183437+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/F52U4HB2DVRE4WGHBPWJC7N7IF","json":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF.json","graph_json":"https://pith.science/api/pith-number/F52U4HB2DVRE4WGHBPWJC7N7IF/graph.json","events_json":"https://pith.science/api/pith-number/F52U4HB2DVRE4WGHBPWJC7N7IF/events.json","paper":"https://pith.science/paper/F52U4HB2"},"agent_actions":{"view_html":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF","download_json":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF.json","view_paper":"https://pith.science/paper/F52U4HB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2620&json=true","fetch_graph":"https://pith.science/api/pith-number/F52U4HB2DVRE4WGHBPWJC7N7IF/graph.json","fetch_events":"https://pith.science/api/pith-number/F52U4HB2DVRE4WGHBPWJC7N7IF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF/action/storage_attestation","attest_author":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF/action/author_attestation","sign_citation":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF/action/citation_signature","submit_replication":"https://pith.science/pith/F52U4HB2DVRE4WGHBPWJC7N7IF/action/replication_record"}},"created_at":"2026-05-18T01:37:38.429307+00:00","updated_at":"2026-05-18T01:37:38.429307+00:00"}