{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C5E5NEZS44TIQJHUEIAQE5V4ZK","short_pith_number":"pith:C5E5NEZS","schema_version":"1.0","canonical_sha256":"1749d69332e7268824f422010276bcca86ff391f2a88b03efe5f2c8a5a4a3542","source":{"kind":"arxiv","id":"1703.03193","version":1},"attestation_state":"computed","paper":{"title":"Embedding Tarskian Semantics in Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.AI","authors_text":"Taisuke Sato","submitted_at":"2017-03-09T09:30:01Z","abstract_excerpt":"We propose a new linear algebraic approach to the computation of Tarskian semantics in logic. We embed a finite model M in first-order logic with N entities in N-dimensional Euclidean space R^N by mapping entities of M to N dimensional one-hot vectors and k-ary relations to order-k adjacency tensors (multi-way arrays). Second given a logical formula F in prenex normal form, we compile F into a set Sigma_F of algebraic formulas in multi-linear algebra with a nonlinear operation. In this compilation, existential quantifiers are compiled into a specific type of tensors, e.g., identity matrices in"},"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":"1703.03193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-03-09T09:30:01Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"c0ae8e479bde0eb82c1a6bd4cf955a40122c2b1c28909d15514d6b081acf06f3","abstract_canon_sha256":"20850caace1827d4123c8eb3a88891bf047a285b590c1911c67c73f4ace92c47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:01.168660Z","signature_b64":"pq4RUuA09I2uYfduA2ts1BW7w5yA+cUJWlGjmen7RQI6DvD/BqcuPpr95pHFhxsY5O1SYX8ck7ycHntYsM4CAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1749d69332e7268824f422010276bcca86ff391f2a88b03efe5f2c8a5a4a3542","last_reissued_at":"2026-05-18T00:49:01.168161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:01.168161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding Tarskian Semantics in Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.AI","authors_text":"Taisuke Sato","submitted_at":"2017-03-09T09:30:01Z","abstract_excerpt":"We propose a new linear algebraic approach to the computation of Tarskian semantics in logic. We embed a finite model M in first-order logic with N entities in N-dimensional Euclidean space R^N by mapping entities of M to N dimensional one-hot vectors and k-ary relations to order-k adjacency tensors (multi-way arrays). Second given a logical formula F in prenex normal form, we compile F into a set Sigma_F of algebraic formulas in multi-linear algebra with a nonlinear operation. In this compilation, existential quantifiers are compiled into a specific type of tensors, e.g., identity matrices in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03193","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":"1703.03193","created_at":"2026-05-18T00:49:01.168232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03193v1","created_at":"2026-05-18T00:49:01.168232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03193","created_at":"2026-05-18T00:49:01.168232+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5E5NEZS44TI","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5E5NEZS44TIQJHU","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5E5NEZS","created_at":"2026-05-18T12:31:08.081275+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/C5E5NEZS44TIQJHUEIAQE5V4ZK","json":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK.json","graph_json":"https://pith.science/api/pith-number/C5E5NEZS44TIQJHUEIAQE5V4ZK/graph.json","events_json":"https://pith.science/api/pith-number/C5E5NEZS44TIQJHUEIAQE5V4ZK/events.json","paper":"https://pith.science/paper/C5E5NEZS"},"agent_actions":{"view_html":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK","download_json":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK.json","view_paper":"https://pith.science/paper/C5E5NEZS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03193&json=true","fetch_graph":"https://pith.science/api/pith-number/C5E5NEZS44TIQJHUEIAQE5V4ZK/graph.json","fetch_events":"https://pith.science/api/pith-number/C5E5NEZS44TIQJHUEIAQE5V4ZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK/action/storage_attestation","attest_author":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK/action/author_attestation","sign_citation":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK/action/citation_signature","submit_replication":"https://pith.science/pith/C5E5NEZS44TIQJHUEIAQE5V4ZK/action/replication_record"}},"created_at":"2026-05-18T00:49:01.168232+00:00","updated_at":"2026-05-18T00:49:01.168232+00:00"}