{"paper":{"title":"Residuated Park Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Zoltan Esik","submitted_at":"2011-02-06T11:08:57Z","abstract_excerpt":"When $L$ is a complete lattice, the collection $\\Mon_L$ of all monotone functions $L^p \\to L^n$, $n,p \\geq 0$, forms a Lawvere theory. We enrich this Lawvere theory with the binary supremum operation $\\vee$, an operation of (left) residuation $\\res$ and the parameterized least fixed point operation $^\\dagger$. We exhibit a system of \\emph{equational} axioms which is sound and proves all valid equations of the theories $\\Mon_L$ involving only the theory operations, $\\vee$ and $^\\dagger$, i.e., all valid equations not involving residuation. We also present an alternative axiomatization, where $^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1139","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"}