{"paper":{"title":"Algebraic Semantics for Nelson's Logic S","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jo\\~ao Marcos, Matthew Spinks, Thiago Nascimento, Umberto Rivieccio","submitted_at":"2018-03-28T20:49:26Z","abstract_excerpt":"Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in \"Negation and separation of concepts in constructive systems\" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content of provable negation statements in mathematics. Motivated by results from Kleene, in \"On the Interpretation of Intuitionistic Number Theory\" (1945), Nelson investigated a more symmetric recursive definition of truth, according to which a formula could be either primitively verified or refuted. The logic S was defined by means of a calculus lacking the contra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10847","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"}