{"paper":{"title":"Representation of Nelson Algebras by Rough Sets Determined by Quasiorders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jouni J\\\"arvinen, S\\'andor Radeleczki","submitted_at":"2010-07-07T17:38:56Z","abstract_excerpt":"In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\\mathbb{RS}$ is a three-valued {\\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\\mathbb{A} \\cong \\mathbb{RS}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1199","kind":"arxiv","version":3},"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"}