{"paper":{"title":"The Complexity of Fuzzy Logic","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Martin Goldstern","submitted_at":"1997-07-16T00:00:00Z","abstract_excerpt":"Lukasiewicz logic is a \"fuzzy\" logic in which truth value can be real numbers in the unit interval.  There are connectives for min, max, addition and complement (1-x).  The \"value\" of a closed formula in a fuzzy (relational model) is defined in the natural way.\n  A formula is called valid iff it has value 1 in every fuzzy model.\n  We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Pi^0_2 set.\n  We also show that if we restrict our attention to the classical language (min, max, complement) then the classically valid formulas are exactly those formulas whose fuzz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9707205","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"}