{"paper":{"title":"Generalising unit-refutation completeness and SLUR via nested input resolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LO","authors_text":"Matthew Gwynne, Oliver Kullmann","submitted_at":"2012-04-29T23:56:03Z","abstract_excerpt":"We introduce two hierarchies of clause-sets, SLUR_k and UC_k, based on the classes SLUR (Single Lookahead Unit Refutation), introduced in 1995, and UC (Unit refutation Complete), introduced in 1994.\n  The class SLUR, introduced in [Annexstein et al, 1995], is the class of clause-sets for which unit-clause-propagation (denoted by r_1) detects unsatisfiability, or where otherwise iterative assignment, avoiding obviously false assignments by look-ahead, always yields a satisfying assignment. It is natural to consider how to form a hierarchy based on SLUR. Such investigations were started in [Cepe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6529","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}