{"paper":{"title":"Residuated operators and Dedekind-MacNeille completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Helmut L\\\"anger, Ivan Chajda, Jan Paseka","submitted_at":"2018-12-22T22:48:49Z","abstract_excerpt":"The concept of operator residuation for bounded posets with unary operation was introduced by the first two authors. It turns out that in some cases when these operators are transformed into lattice terms and the poset ${\\mathbf P}$ is completed into a Dedekind-MacNeille completion $\\BDM(\\mathbf P)$ then the complete lattice $\\BDM(\\mathbf P)$ becomes a residuated lattice with respect to these transformed terms. It is shown that this holds in particular for Boolean posets and for relatively pseudocomplemented posets.\n  More complicated situation is with orthomodular and pseudo-orthomodular pose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09616","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"}