{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T20:45:24Z","timestamp":1772916324618,"version":"3.50.1"},"reference-count":22,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2022-141529NB-C22"],"award-info":[{"award-number":["PID2022-141529NB-C22"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["CUP F53D23011170001"],"award-info":[{"award-number":["CUP F53D23011170001"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["1016"],"award-info":[{"award-number":["1016"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016973","name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100016973","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Approximate Reasoning"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1016\/j.ijar.2025.109565","type":"journal-article","created":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T10:41:29Z","timestamp":1757500889000},"page":"109565","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Unimodular triangulations in \u0141ukasiewicz logic: Complexity bounds of probabilistic coherence"],"prefix":"10.1016","volume":"187","author":[{"given":"Tommaso","family":"Flaminio","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6046-9877","authenticated-orcid":false,"given":"Serafina","family":"Lapenta","sequence":"additional","affiliation":[]},{"given":"Sebastiano","family":"Napolitano","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.ijar.2025.109565_br0010","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.ijar.2009.10.002","article-title":"The coherence of \u0141ukasiewicz assessments is NP-complete","volume":"51","author":"Bova","year":"2010","journal-title":"Int. J. Approx. Reason."},{"key":"10.1016\/j.ijar.2025.109565_br0020","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jcta.2017.02.005","article-title":"Unimodular triangulations of simplicial cones by short vectors","volume":"150","author":"Bruns","year":"2017","journal-title":"J. Comb. Theory, Ser. A"},{"key":"10.1016\/j.ijar.2025.109565_br0030","series-title":"Algebraic Foundations of Many-Valued Reasoning","author":"Cignoli","year":"2000"},{"key":"10.1016\/j.ijar.2025.109565_br0040","article-title":"Combinatorial Convexity and Algebraic Geometry","author":"Ewald","year":"2012"},{"issue":"3","key":"10.1016\/j.ijar.2025.109565_br0050","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s10472-015-9466-6","article-title":"Probabilistic satisfiability: algorithms with the presence and absence of a phase transition","volume":"75","author":"Finger","year":"2015","journal-title":"Ann. Math. Artif. Intell."},{"key":"10.1016\/j.ijar.2025.109565_br0060","series-title":"Automated Reasoning","first-page":"194","article-title":"Probably half true: probabilistic satisfiability over \u0141ukasiewicz infinitely-valued logic","author":"Finger","year":"2018"},{"issue":"7","key":"10.1016\/j.ijar.2025.109565_br0070","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1007\/s10817-020-09558-9","article-title":"Probably partially true: satisfiability for \u0141ukasiewicz infinitely-valued probabilistic logic and related topics","volume":"64","author":"Finger","year":"2020","journal-title":"J. Autom. Reason."},{"issue":"3","key":"10.1016\/j.ijar.2025.109565_br0080","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1017\/S1755020319000546","article-title":"Three characterizations of strict coherence on infinite-valued events","volume":"13","author":"Flaminio","year":"2020","journal-title":"Rev. Symb. Log."},{"issue":"1","key":"10.1016\/j.ijar.2025.109565_br0090","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1017\/jsl.2017.34","article-title":"Strict coherence on many-valued events","volume":"83","author":"Flaminio","year":"2018","journal-title":"J. Symb. Log."},{"key":"10.1016\/j.ijar.2025.109565_br0100","series-title":"Handbook of Mathematical Fuzzy Logic","first-page":"1191","article-title":"States of MV-algebras","volume":"vol. 3","author":"Flaminio","year":"2015"},{"issue":"3","key":"10.1016\/j.ijar.2025.109565_br0110","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1093\/logcom\/exp013","article-title":"Models for many-valued probabilistic reasoning","volume":"21","author":"Flaminio","year":"2009","journal-title":"J. Log. Comput."},{"issue":"23","key":"10.1016\/j.ijar.2025.109565_br0120","doi-asserted-by":"crossref","first-page":"2605","DOI":"10.1016\/j.fss.2007.07.001","article-title":"Complexity of fuzzy probability logics II","volume":"158","author":"H\u00e1jek","year":"2007","journal-title":"Fuzzy Sets Syst."},{"key":"10.1016\/j.ijar.2025.109565_br0130","series-title":"Topology of Numbers","author":"Hatcher","year":"2022"},{"key":"10.1016\/j.ijar.2025.109565_br0140","series-title":"Matrix Analysis","author":"Horn","year":"2012"},{"issue":"3","key":"10.1016\/j.ijar.2025.109565_br0150","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/2268222","article-title":"Fair bets and inductive probabilities","volume":"20","author":"Kemeny","year":"1955","journal-title":"J. Symb. Log."},{"key":"10.1016\/j.ijar.2025.109565_br0160","doi-asserted-by":"crossref","DOI":"10.1016\/j.jpaa.2021.106771","article-title":"The two-sorted algebraic theory of states, and the universal states of MV-algebras","volume":"225","author":"Kroupa","year":"2021","journal-title":"J. Pure Appl. Algebra"},{"issue":"1","key":"10.1016\/j.ijar.2025.109565_br0170","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/BF01053035","article-title":"Averaging the truth-value in \u0141ukasiewicz logic","volume":"55","author":"Mundici","year":"1995","journal-title":"Stud. Log."},{"key":"10.1016\/j.ijar.2025.109565_br0180","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.ijar.2006.04.004","article-title":"Bookmaking over infinite-valued events","volume":"43","author":"Mundici","year":"2006","journal-title":"Int. J. Approx. Reason."},{"key":"10.1016\/j.ijar.2025.109565_br0190","series-title":"Advanced \u0141ukasiewicz Calculus and MV-Algebras","author":"Mundici","year":"2011"},{"key":"10.1016\/j.ijar.2025.109565_br0200","series-title":"The Uncertain Reasoner's Companion: A Mathematical Perspective","author":"Paris","year":"1994"},{"key":"10.1016\/j.ijar.2025.109565_br0210","series-title":"ISIPTA '01, Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications","first-page":"301","article-title":"A note on the Dutch book method","author":"Paris","year":"2001"},{"key":"10.1016\/j.ijar.2025.109565_br0220","series-title":"Unimodular Covers and Triangulations of Lattice Polytopes","author":"von Thaden","year":"2008"}],"container-title":["International Journal of Approximate Reasoning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X25002063?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X25002063?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T03:11:11Z","timestamp":1772853071000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0888613X25002063"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12]]},"references-count":22,"alternative-id":["S0888613X25002063"],"URL":"https:\/\/doi.org\/10.1016\/j.ijar.2025.109565","relation":{},"ISSN":["0888-613X"],"issn-type":[{"value":"0888-613X","type":"print"}],"subject":[],"published":{"date-parts":[[2025,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Unimodular triangulations in \u0141ukasiewicz logic: Complexity bounds of probabilistic coherence","name":"articletitle","label":"Article Title"},{"value":"International Journal of Approximate Reasoning","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ijar.2025.109565","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"109565"}}