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In this paper we expand the cognitive power of $IFOL_B$ by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the $IFOL_B$. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of $IFOL_B$ predicates. The computation of probability density function $KI$ in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.","title":"Probabilistic Extension of Neuro-Symbolic AGI Robots based on Belnap's Typed Intensional FOL","url":"https://arxiv.org/abs/2607.13073","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.13073v1 Announce Type: new \nAbstract: Neuro-symbolic AI based on $IFOL_B$ is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference. In this paper we expand the cognitive power of $IFOL_B$ by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the $IFOL_B$. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of $IFOL_B$ predicates. The computation of probability density function $KI$ in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.","title":"Probabilistic Extension of Neuro-Symbolic AGI Robots based on Belnap's Typed Intensional FOL","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-16T04:44:04Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.13073"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:eb6d05071a862b3dac9d4a83a50b16c0e28493402c6256c443cd8e4633aa88e12719857cb96e97d9fe5e3cdd0547a102b86cb1b1204a77c33ee25656bb6b1d08","signer":"crovia.substrate","subject":{"observed_at":"2026-07-16T04:44:04Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.13073"},"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":"038142492d7b74a35ae11f4b93af53f1a044b5ec19d747b9f0c6da8f3ad09347","leaf_index":319736,"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":"3f64a779b51902031fb5c5606a0834f04b5cad484d50a03145aa65ee31d3e6f0","side":"right"},{"sibling":"9d6c52010085a98b5982ba66700e84cc15c2d031e07de2880f94018a44a3261a","side":"right"},{"sibling":"042216be8f1390734e4d6264d09d202f2a614df0f7de1e7542d731e2df804b7f","side":"right"},{"sibling":"efeb15d5b0168c0aa2b85435d22ce97e6ac198a2cec24d3b203a2b0ff6d30bfa","side":"left"},{"sibling":"c102cb84d4b02596e0aa505833d465ac34651eb5e6bd0b86a17b94e0320a1a42","side":"left"},{"sibling":"5f09524f27542518a837cee9805679944758044c4c54016d2114eb8d02e92163","side":"left"},{"sibling":"948d117a11620458d1044803bd6825a7bc2d2ac86a218e2f4ea410dd3ad53561","side":"left"},{"sibling":"292d0fe0da603c8c11771c0328ba02ed01ebc5a474773ed9b5606fb2c6cf0418","side":"left"},{"sibling":"51487156367f8a33b565076edd9ecd8052c61ddf8b0243d35e3475d37deca00a","side":"right"},{"sibling":"1290775fa2a1fe2079ed83a9c60b8cb479714b6312967daa62f6a91dbbe1cac9","side":"right"},{"sibling":"95977bf2fb44d423026e874e6c275f78b1cf48666d2c472c5e4603d16f4faf7f","side":"right"},{"sibling":"6b83879fdb76b5b7270071f1edfe4d1a059fa9b92653e70fc8c8893214b8f237","side":"right"},{"sibling":"ff49c1d8749b258f58cc33cfaf20d723098ed6860fb62a6779db960d6250915b","side":"right"},{"sibling":"34d85f6ad6cc7dfa79d90e2b9ff99a561bcdc75b0301bbbd3e83861f54535c1e","side":"left"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"3ee6ab8db1878db0b324dd807ca233edd472899b8e90d2c5e018848ea5d12d99","side":"right"},{"sibling":"73a8d1605c15a74de720f0c54b5b4567e3eb8b5999bd8812dc66eedc461540fa","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":320080,"merkle_root":"1e159bceacfdb1f3c930dae410f8759ddc4c762abcfa4a257b150d6f44ab16e0","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260716T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-16T05:38:31Z","sig_algorithm":"ed25519","signature":"c1cd1fc5704d4fec4dee47b29a0e9877f8cfb41eb61dcfd783d82344a15f6e44d80d6cd5128849547b62fe9d9724fc71433319ab6030445b4ac1c9e6bf8a3709","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_6956b639c1239c38d9e52f758636142aae216b8ea2d7ebdb6840aa43780c4caa"}}