{"paper":{"title":"Interval MV-algebras and generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Daniele Mundici, Leonardo Manuel Cabrer","submitted_at":"2014-03-04T20:33:01Z","abstract_excerpt":"For any MV-algebra $A$ we equip the set $I(A)$ of intervals in $A$ with pointwise \\L ukasiewicz negation $\\neg x=\\{\\neg \\alpha\\mid \\alpha\\in x\\}$, (truncated) Minkowski sum, $x\\oplus y=\\{\\alpha\\oplus \\beta\\mid \\alpha \\in x,\\,\\,\\beta\\in y\\}$, pointwise \\L ukasiewicz conjunction $x\\odot y=\\neg(\\neg x\\oplus \\neg y)$, the operators $\\Delta x=[\\min x,\\min x]$, $\\nabla x=[\\max x,\\max x]$, and distinguished constants $0=[0,0],\\,\\, 1=[1,1],\\,\\,\\, \\mathsf{i} = A$. We list a few equations satisfied by the algebra $\\mathcal I(A)=(I(A),0,1,\\mathsf{i},\\neg,\\Delta,\\nabla,\\oplus,\\odot)$, call IMV-algebra eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0932","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"}