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Answering existential first-order queries with $k$ free variables (i.e., $\\text{EFO}_k$ queries) is a crucial yet challenging problem, as it requires ranking answer tuples in $\\mathcal{E}^k$, where $\\mathcal{E}$ denotes the entity set of a KG. This quickly becomes intractable as $k$ grows. Consequently, existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of tuples. Building on neural symbolic search for $\\text{EFO}_1$ queries, we propose Neural Scalable Symbolic Search (NS3), a budgeted framework that approximates joint ranking without enumerating $\\mathcal{E}^k$. NS3 (i) answers marginalized sub-queries to obtain necessary candidate sets, (ii) merges multiple free variables into hypernodes whose domains ar","title":"Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables","url":"https://arxiv.org/abs/2605.25985","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.25985v1 Announce Type: new \nAbstract: Complex Query Answering (CQA) is a fundamental knowledge representation and reasoning task over incomplete knowledge graphs (KGs). Answering existential first-order queries with $k$ free variables (i.e., $\\text{EFO}_k$ queries) is a crucial yet challenging problem, as it requires ranking answer tuples in $\\mathcal{E}^k$, where $\\mathcal{E}$ denotes the entity set of a KG. This quickly becomes intractable as $k$ grows. Consequently, existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of tuples. Building on neural symbolic search for $\\text{EFO}_1$ queries, we propose Neural Scalable Symbolic Search (NS3), a budgeted framework that approximates joint ranking without enumerating $\\mathcal{E}^k$. NS3 (i) answers marginalized sub-queries to obtain necessary candidate sets, (ii) merges multiple free variables into hypernodes whose domains ar","title":"Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-26T04:43:39Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.25985"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:20029eac5954ba216ccd006f9c768c78d3ca67745146c090113ebe31ebaed2fa4d32e7999ecb479da8a23d5d2f679a03176089eb26e4302a0eee64476b4d1c08","signer":"crovia.substrate","subject":{"observed_at":"2026-05-26T04:43:39Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.25985"},"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":"70d9a3b0189f7b7edccbdb29ce0a020d939521364a7f928536e72441ef64fe42","leaf_index":151446,"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":"dd11ecff4e4022879174f381e0908348d0b5d76c1f84eeb0c7d84f3324c88fd2","side":"right"},{"sibling":"0cef6babd82e621ae9bcb92566139439aa4709af2df1c7e9be200f925adf81bd","side":"left"},{"sibling":"b73c99703aba56f7427dddf22eff615d8cd5163278eadddc8f8ed41a00a3c335","side":"left"},{"sibling":"0e3fb3fecd48884497f86ad183c5f9edf3422d48e36b81d1028bc07219d92018","side":"right"},{"sibling":"2cddedae1dda32c5f7901061b726d975f6828d607035f541d26fdae166ad558b","side":"left"},{"sibling":"783493de26a2f644dce98d98fb3cb27e4f417c98333b4e0129841981d3ac4f6a","side":"right"},{"sibling":"e5e0e8d837a1eb5f20af10583ad77cd53168b9effa387448a6f44515c3f60f17","side":"right"},{"sibling":"12607c0dd56c2db51bf46dd95ab0fe795f3f832d068cd7268fed3aeeb8a7cc29","side":"left"},{"sibling":"a808644c9a09dd75253c6c0ba9275dc94a6b6451ad5184ebdafda4a2722b36a5","side":"left"},{"sibling":"fdd22ebd87e5ba37d1153e47753a63818abb25df8fe45dbf735ba5c512c3355b","side":"left"},{"sibling":"cf593c482d17d202b94914915d0c65fb8713053548db64771d0ec5dbb404a07f","side":"left"},{"sibling":"134949308b15cffd6792ee2cf678119af34d69a64764d7c89cd47573c94e1cda","side":"left"},{"sibling":"e20a7391fed5b5f3b675af68344a3f5b050d6701e127b7db010af3941e59dfdb","side":"right"},{"sibling":"e5893793e3591ed7f5e58ca94ffcfba46bb30f69fb1c25d5ba8ef49eb99f9126","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"e3eecaf996dbe7229a7bb1d234c97aea97a252c5f7c89f8547b6d091db0f0e40","side":"right"},{"sibling":"55bcbd4da3e20d93931f7e58673f10232e81a5b1514d7396cb4b71e8f95788d0","side":"right"},{"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":152106,"merkle_root":"ac5182c6f3dd09931f2a689df5f4be36df7b55e55bcf106e195671f5ed55fd8f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260526T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-26T05:37:34Z","sig_algorithm":"ed25519","signature":"a401243fbd2c077d29a623c6ef616c78fbd5c8ce1930afa7af7165b2386e5a8cf15d5094983a1c962e71b27b911a3f3ce09c8cfab9393be2ce5ce8ee6513da06","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_09c9a4fcbb43ca213f26f1b5ee4370f213d5b2f0103cd319b59344cff2726281"}}