{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T10:48:09Z","timestamp":1776077289470,"version":"3.50.1"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"9","license":[{"start":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T00:00:00Z","timestamp":1652745600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This work concerns the representation of a class of continuous functions into Logic, so that one may automatically reason about properties of these functions using logical tools. Rational McNaughton functions may be implicitly represented by logical formulas in \u0141ukasiewicz Infinitely-valued Logic by constraining the set of allowed valuations; such a restriction contemplates only those valuations that satisfy specific formulas. This work investigates two approaches to such depiction, called representation modulo satisfiability. Furthermore, a polynomial-time algorithm that builds this representation is presented, producing a pair of formulas consisting of the representative formula and the constraining one, given as input a rational McNaughton function in a suitable encoding. An implementation of the algorithm is discussed.<\/jats:p>","DOI":"10.1017\/s096012952200010x","type":"journal-article","created":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T11:34:18Z","timestamp":1652787258000},"page":"1119-1144","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["Efficient representation of piecewise linear functions into \u0141ukasiewicz logic modulo satisfiability"],"prefix":"10.1017","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4448-5364","authenticated-orcid":false,"given":"Sandro","family":"Preto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcelo","family":"Finger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,5,17]]},"reference":[{"key":"S096012952200010X_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08867-9_49"},{"key":"S096012952200010X_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/NAFIPS.2002.1018111"},{"key":"S096012952200010X_ref17","unstructured":"Gamrath, G. , Anderson, D. , Bestuzheva, K. , Chen, W.-K. , Eifler, L. , Gasse, M. , Gemander, P. , Gleixner, A. , Gottwald, L. , Halbig, K. , Hendel, G. , Hojny, C. , Koch, T. , Bodic, P. L. , Maher, S. J. , Matter, F. , Miltenberger, M. , M\u00fchmer, E. , M\u00fcller, B. , Pfetsch, M. , Schl\u00f6sser, F. , Serrano, F. , Shinano, Y. , Tawfik, C. , Vigerske, S. , Wegscheider, F. , Weninger, D. and Witzig, J. (2020). The SCIP optimization suite 7.0. Technical report, Optimization Online."},{"key":"S096012952200010X_ref20","doi-asserted-by":"publisher","DOI":"10.2307\/2268660"},{"key":"S096012952200010X_ref11","doi-asserted-by":"crossref","unstructured":"Di Nola, A. and Leu\u015ftean, I. (2011). Riesz MV-algebras and their logic. In: Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), Atlantis Press, 140\u2013145.","DOI":"10.2991\/eusflat.2011.125"},{"key":"S096012952200010X_ref8","volume-title":"Introduction to Linear Optimization","author":"Bertsimas","year":"1997"},{"key":"S096012952200010X_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90083-1"},{"key":"S096012952200010X_ref10","volume-title":"Trends in Logic","author":"Cignoli","year":"2000"},{"key":"S096012952200010X_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2012.63"},{"key":"S096012952200010X_ref22","doi-asserted-by":"publisher","DOI":"10.2307\/2275410"},{"key":"S096012952200010X_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2020.08.009"},{"key":"S096012952200010X_ref26","doi-asserted-by":"publisher","DOI":"10.1109\/CDC40024.2019.9030119"},{"key":"S096012952200010X_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050173"},{"key":"S096012952200010X_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/aama.1998.0581"},{"key":"S096012952200010X_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-94205-6_14"},{"key":"S096012952200010X_ref18","first-page":"579","article-title":"Rational \u0141ukasiewicz logic and DMV-algebras","volume":"11","author":"Gerla","year":"2001","journal-title":"Neural Network World"},{"key":"S096012952200010X_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80131-5"},{"key":"S096012952200010X_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1348-z"},{"key":"S096012952200010X_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/0895-7177(90)90090-A"},{"key":"S096012952200010X_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10817-020-09558-9"},{"key":"S096012952200010X_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(99)00195-8"},{"key":"S096012952200010X_ref2","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2001.924596"},{"key":"S096012952200010X_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1769-0_14"},{"key":"S096012952200010X_ref7","unstructured":"Barrett, C. , Fontaine, P. and Tinelli, C. (2016). The satisfiability modulo theories library (SMT-LIB). www.SMT-LIB.org."},{"key":"S096012952200010X_ref5","first-page":"777","article-title":"An algorithm for the automatic generation of a logical formula representing a control law","volume":"10","author":"Amato","year":"2000","journal-title":"Neural Network World"},{"key":"S096012952200010X_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2015.10"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096012952200010X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,29]],"date-time":"2023-03-29T02:33:34Z","timestamp":1680057214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096012952200010X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,17]]},"references-count":26,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["S096012952200010X"],"URL":"https:\/\/doi.org\/10.1017\/s096012952200010x","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,17]]},"assertion":[{"value":"\u00a9 The Author(s), 2022. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}