{"paper":{"title":"Ordinal and Horizontal Sums Constructing PBZ*-lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Claudia Mure\\c{s}an, Francesco Paoli, Roberto Giuntini","submitted_at":"2018-11-05T17:35:56Z","abstract_excerpt":"PBZ*-lattices are algebraic structures related to quantum logics, which consist of bounded lattices endowed with two kinds of complements, named {\\em Kleene} and {\\em Brouwer}, such that the Kleene complement satisfies a weakening of the orthomodularity condition and the De Morgan laws, while the Brouwer complement only needs to satisfy the De Morgan laws for the pairs of elements with their Kleene complements. PBZ*-lattices form a variety $\\mathbb{PBZL}^{\\ast }$, which includes the variety $\\mathbb{OML}$ of orthomodular lattices (considered with an extended signature, by letting their two com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01869","kind":"arxiv","version":2},"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"}