{"paper":{"title":"A representation of antimatroids by Horn rules and its application to educational systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai, Hiyori Yoshikawa, Kazuhisa Makino","submitted_at":"2015-08-22T03:50:10Z","abstract_excerpt":"We study a representation of an antimatroid by Horn rules, motivated by its recent application to computer-aided educational systems. We associate any set $\\mathcal{R}$ of Horn rules with the unique maximal antimatroid $\\mathcal{A}(\\mathcal{R})$ that is contained in the union-closed family $\\mathcal{K}(\\mathcal{R})$ naturally determined by ${\\cal R}$. We address algorithmic and Boolean function theoretic aspects on the association ${\\cal R} \\mapsto \\mathcal{A}(\\mathcal{R})$, where ${\\cal R}$ is viewed as the input. We present linear time algorithms to solve the membership problem and the infer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05465","kind":"arxiv","version":4},"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"}