{"paper":{"title":"Hereditary First-Order Logic: the tractable quantifier prefix classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.LO"],"primary_cat":"math.LO","authors_text":"Manuel Bodirsky, Santiago Guzm\\'an-Pro","submitted_at":"2024-11-16T18:50:15Z","abstract_excerpt":"Many computational problems can be modelled as the class of all finite structures $\\mathbb A$ that satisfy a fixed first-order sentence $\\phi$ hereditarily, i.e., we require that every (induced) substructure of $\\mathbb A$ satisfies $\\phi$. We call the corresponding computational problem the hereditary model checking problem for $\\phi$, and denote it by Her$(\\phi)$.\n  We present a complete description of the quantifier prefixes for $\\phi$ such that Her$(\\phi)$ is in P; we show that for every other quantifier prefix there exists a formula $\\phi$ with this prefix such that Her$(\\phi)$ is coNP-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10860","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.10860/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}