{"paper":{"title":"{\\L}ukasiewicz {\\mu}-calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alex Simpson, Matteo Mio","submitted_at":"2015-10-03T09:11:59Z","abstract_excerpt":"The paper explores properties of the {\\L}ukasiewicz {\\mu}-calculus, or {\\L}{\\mu} for short, an extension of {\\L}ukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe that {\\L}{\\mu} terms, with $n$ variables, define monotone piecewise linear functions from $[0, 1]^n$ to $[0, 1]$. Two effective procedures for calculating the output of {\\L}{\\mu} terms on rational inputs are presented. We then consider the {\\L}ukasiewicz modal {\\mu}-calculus, which is obtained by adding box and diamond modalities to {\\L}{\\mu}. Alternatively, it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00797","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"}