{"paper":{"title":"Drawing Sound Conclusions from Unsound Premises","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Claudia Picardi, Daniele Mundici","submitted_at":"2011-09-05T14:37:27Z","abstract_excerpt":"Given sets $\\Phi_1=\\{\\phi_{11},...,\\phi_{1u(1)}\\}, ...,\\Phi_{z}=\\{\\phi_{z1},...,\\phi_{zu(z)}\\}$ of boolean formulas, a formula $\\omega$ follows from the conjunction $\\bigwedge\\Phi_i= \\bigwedge \\phi_{ij}$ iff $\\neg \\omega\\wedge \\bigwedge_{i=1}^z \\Phi_i$ is unsatisfiable.\n  Now assume that, given integers $0\\leq e_i < u(i)$, we must check if $\\neg \\omega\\wedge \\bigwedge_{i=1}^z \\Phi'_i$ remains unsatisfiable, where $\\Phi'_i\\subseteq \\Phi_i$ is obtained by deleting $\\,\\,e_{i}$ arbitrarily chosen formulas of $\\Phi_i$, for each $i=1,...,z.$\n  Intuitively, does $\\omega$ {\\it stably} follow, after re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0915","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"}