{"paper":{"title":"Finding Minimal Cost Herbrand Models with Branch-Cut-and-Price","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"James Cussens","submitted_at":"2018-08-14T15:45:01Z","abstract_excerpt":"Given (1) a set of clauses $T$ in some first-order language $\\cal L$ and (2) a cost function $c : B_{{\\cal L}} \\rightarrow \\mathbb{R}_{+}$, mapping each ground atom in the Herbrand base $B_{{\\cal L}}$ to a non-negative real, then the problem of finding a minimal cost Herbrand model is to either find a Herbrand model $\\cal I$ of $T$ which is guaranteed to minimise the sum of the costs of true ground atoms, or establish that there is no Herbrand model for $T$. A branch-cut-and-price integer programming (IP) approach to solving this problem is presented. Since the number of ground instantiations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04758","kind":"arxiv","version":1},"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"}