{"paper":{"title":"The differential semantics of Lukasiewicz syntactic consequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Daniele Mundici","submitted_at":"2012-07-24T14:34:10Z","abstract_excerpt":"The classical condition \"$\\phi$ is a semantic consequence of $\\Theta$\" in infinite-valued propositional \\L ukasiewicz logic \\L$_\\infty$ is refined using enriched valuations that take into account the effect on $\\phi$ of the stability of the truth-value of all $\\theta\\in \\Theta$ under small perturbations (or, measurement errors) of the models of $\\Theta$. The differential properties of the functions represented by $\\phi$ and by all $\\theta\\in \\Theta$ naturally lead to a new notion of semantic consequence $\\models_\\partial$ that turns out to coincide with syntactic consequence $\\vdash$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5713","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"}