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We show two methodological limitations that prevent supervised deep learning from reaching the symbolic-level syllogistic reasoning: (1) training data can not distinguish all 24 types of valid syllogistic reasoning; (2) end-to-end mapping from premises to conclusion introduces contradictory training targets between neural components for pattern recognition and logical reasoning. Beside theoretical analysis, we experimentally illustrate that Euler Net cannot achieve rigorous syllogistic reasoning. We further challenge the most recent ChatGPTs (GPT-5-nano and GPT-5) to determine the satisfiability of syllogistic statements in four surfa","title":"Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law","url":"https://arxiv.org/abs/2606.26454","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.26454v1 Announce Type: new \nAbstract: Sphere neural networks have achieved symbolic level syllogistic reasoning without training data, raising the question of where the limit of the scaling law for logical reasoning lies, i.e., whether data-driven machine learning systems can achieve the same level by increasing training data and training time. We show two methodological limitations that prevent supervised deep learning from reaching the symbolic-level syllogistic reasoning: (1) training data can not distinguish all 24 types of valid syllogistic reasoning; (2) end-to-end mapping from premises to conclusion introduces contradictory training targets between neural components for pattern recognition and logical reasoning. Beside theoretical analysis, we experimentally illustrate that Euler Net cannot achieve rigorous syllogistic reasoning. We further challenge the most recent ChatGPTs (GPT-5-nano and GPT-5) to determine the satisfiability of syllogistic statements in four surfa","title":"Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-26T04:43:58Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.26454"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:8e92c8881c59d52c359437577b7a0db35ef611d010d00d018287889cae8b19f3252d7a954588cae5bd2162e8d6e3d6fe7da771682b9ed1008441f38e311e0d05","signer":"crovia.substrate","subject":{"observed_at":"2026-06-26T04:43:58Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.26454"},"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":"514faa7be1ebab60e17ad1f1def583d4d3b2477ca13a6a0703838cbcc2bf5f40","leaf_index":251008,"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":"cc61a6898982f9d7493c3ca8dd761b3dab14b7c539146d0961d6028c0d39e8b7","side":"right"},{"sibling":"0c237a1e4d80f124eb1f155526c8cdae91448c6284abe1f5536bde5ee62a1a81","side":"right"},{"sibling":"af1e9f14500d33d160b040ab7bcf0b2d8a238fbb5fbbc973633618e864d7eabf","side":"right"},{"sibling":"1b25eca609e57a2e5fed4ed45bee248bd61bc67bac9874a304f52f24995713c5","side":"right"},{"sibling":"5d5cfd235a8a09a28ba993bff9c727d0bc310ef2df9239d866300e52e881cebb","side":"right"},{"sibling":"9ebd81705c7903e17631922173cae6c0494ad086614d7cd5aff5313ac94a9893","side":"right"},{"sibling":"b31fd8919314f43e5528d32d692e1d0c9345f86173f69bd11bcf95d27af3147a","side":"right"},{"sibling":"762a50202e5bb846bfb5afec2f3cc80d9313546598c6c53f53acc51c6325b763","side":"left"},{"sibling":"e276c2896e885a069398e8350a2d9aae49ed0ab34771e352045341312283b40a","side":"right"},{"sibling":"b6709caadc8510310ee2ec0b66d1058fcad31c91c65cc2bad6f46a693d553580","side":"right"},{"sibling":"a72c3b8804a37d1a9d18e02e6fdb048bc8ea6b0746909cd2de10bdbabc793737","side":"left"},{"sibling":"803703dc2c50a646fa77b57c0056e9a5126611ba4bcde0d6013ccd6b2d44bdbf","side":"right"},{"sibling":"e78f244b1b8df6d5e3fdc6dd76b5c27d4e6fe3b93b8cd61355497b63d7e4cfe8","side":"left"},{"sibling":"6167cb552ed6871fbf0afcf3db01d1017af7d472b136fcbe5404d1df09f41cc1","side":"right"},{"sibling":"f29798d8bb6aa9900eab878992d9ff0c53266debd87472f31ab26a6a3fb55880","side":"left"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","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":251380,"merkle_root":"e042805d07cd8dc777d49695ad78b8d4ec9721df271ff0245d7706773c30b4a5","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260626T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-26T05:37:59Z","sig_algorithm":"ed25519","signature":"c68a6e827804771acd244208495c5e35c6f417307db3c76192f038dedaa5b5f86e019074a3bea353357ff7457924c4f7907832638bb9a4d3d18e7a7f50c6a10b","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_a525986bc160a9971351bea8e368708c723593be2f39a974a2c03d1c6eeff7cc"}}