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Language models can propose such structures from text, but their outputs can still be unsupported or inconsistent. This paper proposes a retrieval-augmented small language model (SLM) framework that uses formal concept analysis (FCA) as a symbolic verification loop for knowledge expansion. Starting from seed attributes, FCA proposes implications over a growing formal context. A retrieval-grounded SLM oracle then validates each implication or returns a counterexample. The oracle also supports incidence judgments, consistency checks, and attribute proposals, making accepted implications, counterexamples, contradictions, and corrections inspectable. In a rare ataxia setting constructed from Orphadata resources, retrieval-grounded 10-seed runs obtain relation F1 of 0.29-0.52 and closure-based implication F1 of 0.","title":"Verifiable Knowledge Expansion through Retrieval-Grounded Formal Concept Analysis","url":"https://arxiv.org/abs/2607.01773","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.01773v1 Announce Type: new \nAbstract: Ontology construction requires deciding which objects, attributes, and structural relations should be accepted as valid knowledge. Language models can propose such structures from text, but their outputs can still be unsupported or inconsistent. This paper proposes a retrieval-augmented small language model (SLM) framework that uses formal concept analysis (FCA) as a symbolic verification loop for knowledge expansion. Starting from seed attributes, FCA proposes implications over a growing formal context. A retrieval-grounded SLM oracle then validates each implication or returns a counterexample. The oracle also supports incidence judgments, consistency checks, and attribute proposals, making accepted implications, counterexamples, contradictions, and corrections inspectable. In a rare ataxia setting constructed from Orphadata resources, retrieval-grounded 10-seed runs obtain relation F1 of 0.29-0.52 and closure-based implication F1 of 0.","title":"Verifiable Knowledge Expansion through Retrieval-Grounded Formal Concept Analysis","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-03T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.01773"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:9a9126a8a8d260b6df3eda1f4aad5c1d431e45b1e4b0746d95ad47252711cb32bb989b23f53155e7c45fbba82ab8e20c7280e42cd8644d426b29065b813ae206","signer":"crovia.substrate","subject":{"observed_at":"2026-07-03T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.01773"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"ecd9a366fa65b02776d8dd7d3a2c6bcd4f3fc53c490d36a11d0f6b6f392ed1f0","leaf_index":275371,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"20a6075c9932b5f55e2c107e0d3ecc1db897854a4b3df24a39029d5d78664e30","side":"left"},{"sibling":"5a86614c3e96414ff9a23684f5b9fa24cabb82a38a3ff07705c629844e2b3318","side":"left"},{"sibling":"abd5e79fb318f5f7747f2fef2a03f7ec61e848911f71eb8600ac94354926d2cb","side":"right"},{"sibling":"33b50bcef943992f4e461c1aaafdc235e04fa9ceb2786ece0a2538075df1af28","side":"left"},{"sibling":"d72aa1f925dab408f8a7feb7ee9f4fcbb7643a503e99fe6c7bef38ec0e25984f","side":"right"},{"sibling":"1031e5965521cd2d57d0a685e70068eda5d4e9645dbb1aca1d0133d801ecf1e2","side":"left"},{"sibling":"90e9fb2a20374342836f11695e291756a1f8a0197a80f5da7958594a976dd668","side":"right"},{"sibling":"fd055e725b36f5bebbaeb18583f9d7011c4d8c2a608a11cbd2c166cd895e7a85","side":"left"},{"sibling":"e1a65581e9d68211aa8ba0d138c8d2a4e80afd551e6d1b00c4575c39085df705","side":"left"},{"sibling":"92c062f377cd53076b8dfe55c25ab217059e20113433673cc5747b9348b07e01","side":"left"},{"sibling":"e36f7633c67452f41a7377a7bec9b2d454442688d26539321eebf92cae9db0f0","side":"right"},{"sibling":"4dbd8247ba08a5432c7d6540711da9acb2f59e6189865aa8552dee37f69286a9","side":"right"},{"sibling":"41cd1885dc3fcb51e49eeb887d6d22ec2cfa58df0e4f8d7c7dddf3a1b0ce8249","side":"left"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"723981908169653ca6d835aa9b8381a8c7ad3e3e3830d0792bc32032cda615ee","side":"right"},{"sibling":"c0594fa1ee81d5f019cccc7b5e51af603c6d7e43995498c451012060c7d06165","side":"right"},{"sibling":"4de6a2fb22efbb50c84dc62abeb0f2cbc8c663a9540aeba9e758ebfdfe3e86dd","side":"right"},{"sibling":"fdbb3519f8dc411a4043dfb5abdbfea5441e130326183ac2247c42584033f152","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":275799,"merkle_root":"2581d0d6e5fa345cdf2e8ab3b191ace76d6b14189901ab0e4c2291ca1d1ae1e6","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260703T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-03T05:38:09Z","sig_algorithm":"ed25519","signature":"e44a386a5ae00c0e7fc67b1179bb9060bf0fefc006e454fec70e27668182ff497d1e2faf0c3b22de0917beefb7c80e880dae925a3f67e1b16aa0eb44bf947407","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_133f6d73ec322ae343e7a90b980324a221a13a9399152d57df8f8260057d9992"}}