{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:O5NVYD6DKD7ZQVVXHIMBE6QPCQ","short_pith_number":"pith:O5NVYD6D","schema_version":"1.0","canonical_sha256":"775b5c0fc350ff9856b73a18127a0f140e6662fad53f0d80070460f11964b39f","source":{"kind":"arxiv","id":"1904.03934","version":1},"attestation_state":"computed","paper":{"title":"On matrices and $K$-relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DB","authors_text":"Jan Van den Bussche, Marc Gyssens, Robert Brijder","submitted_at":"2019-04-08T10:26:35Z","abstract_excerpt":"We show that the matrix query language $\\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation arities to two. We then proceed to show that $\\mathsf{MATLANG}$ can express all matrix queries expressible in the positive relational algebra on $K$-relations, when intermediate arities are restricted to three. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to fi"},"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":"1904.03934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2019-04-08T10:26:35Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"536f45873944c25e5c27142bffe6903686da35f8c79838fdabc385647d29e2bc","abstract_canon_sha256":"00097a10b130b697e58ea25e3d3e6d4c32c4574754b6cd013d779a6e650cdbd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:07.640619Z","signature_b64":"Yp3MMgnvfxMb9K0v6YJ4zygGbc8st7bvD3rtbs8LbmHdOzIpsirBVLAgBdDpcKa+0O9VEChPI+8pL7pOcQBeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"775b5c0fc350ff9856b73a18127a0f140e6662fad53f0d80070460f11964b39f","last_reissued_at":"2026-05-17T23:49:07.640155Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:07.640155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On matrices and $K$-relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.DB","authors_text":"Jan Van den Bussche, Marc Gyssens, Robert Brijder","submitted_at":"2019-04-08T10:26:35Z","abstract_excerpt":"We show that the matrix query language $\\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation arities to two. We then proceed to show that $\\mathsf{MATLANG}$ can express all matrix queries expressible in the positive relational algebra on $K$-relations, when intermediate arities are restricted to three. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03934","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":"1904.03934","created_at":"2026-05-17T23:49:07.640230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03934v1","created_at":"2026-05-17T23:49:07.640230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03934","created_at":"2026-05-17T23:49:07.640230+00:00"},{"alias_kind":"pith_short_12","alias_value":"O5NVYD6DKD7Z","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"O5NVYD6DKD7ZQVVX","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"O5NVYD6D","created_at":"2026-05-18T12:33:24.271573+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/O5NVYD6DKD7ZQVVXHIMBE6QPCQ","json":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ.json","graph_json":"https://pith.science/api/pith-number/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/graph.json","events_json":"https://pith.science/api/pith-number/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/events.json","paper":"https://pith.science/paper/O5NVYD6D"},"agent_actions":{"view_html":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ","download_json":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ.json","view_paper":"https://pith.science/paper/O5NVYD6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03934&json=true","fetch_graph":"https://pith.science/api/pith-number/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/action/storage_attestation","attest_author":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/action/author_attestation","sign_citation":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/action/citation_signature","submit_replication":"https://pith.science/pith/O5NVYD6DKD7ZQVVXHIMBE6QPCQ/action/replication_record"}},"created_at":"2026-05-17T23:49:07.640230+00:00","updated_at":"2026-05-17T23:49:07.640230+00:00"}