{"paper":{"title":"Set-like operations on propositional logic programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Every minimalist Horn logic program decomposes into Krom programs so its least model can be recovered exactly from the least models of those components.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Christian Anti\\'c","submitted_at":"2026-05-05T10:39:59Z","abstract_excerpt":"A systematic algebraic framework for composing and decomposing logic programs is currently missing, limiting our ability to analyze and construct programs in a modular way. In this paper, we introduce set-like operations for (propositional Horn) logic programs that allow for a structured manipulation of rule bodies. Our main technical result shows that programs can be decomposed into simpler components in such a way that their least model semantics can be reconstructed or approximated from the semantics of these components. In particular, we prove that every minimalist program can be decompose"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"every minimalist program can be decomposed into Krom programs -- consisting only of rules with at most one body atom -- such that its least model can be computed from the least models of its components","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The definitions of 'minimalist program' and 'Krom program' together with the set-like operations allow exact reconstruction of least-model semantics for the minimalist case; this assumption is stated as the main technical result but its precise scope and any hidden restrictions on rule forms are not detailed in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Propositional Horn logic programs can be decomposed into Krom programs such that least models of the original programs can be reconstructed or approximated from the least models of the components.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every minimalist Horn logic program decomposes into Krom programs so its least model can be recovered exactly from the least models of those components.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d68b54595b49f6cb0271a7ac0944567c528fd6b2211611ea8236d9015acf4e84"},"source":{"id":"2605.03613","kind":"arxiv","version":2},"verdict":{"id":"caca9d61-43ce-4779-bea5-480969e22551","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T13:32:29.320210Z","strongest_claim":"every minimalist program can be decomposed into Krom programs -- consisting only of rules with at most one body atom -- such that its least model can be computed from the least models of its components","one_line_summary":"Propositional Horn logic programs can be decomposed into Krom programs such that least models of the original programs can be reconstructed or approximated from the least models of the components.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The definitions of 'minimalist program' and 'Krom program' together with the set-like operations allow exact reconstruction of least-model semantics for the minimalist case; this assumption is stated as the main technical result but its precise scope and any hidden restrictions on rule forms are not detailed in the abstract.","pith_extraction_headline":"Every minimalist Horn logic program decomposes into Krom programs so its least model can be recovered exactly from the least models of those components."},"integrity":{"clean":false,"summary":{"advisory":1,"critical":1,"by_detector":{"doi_compliance":{"total":2,"advisory":1,"critical":1,"informational":0}},"informational":0},"endpoint":"/pith/2605.03613/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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