{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T07:15:26Z","timestamp":1783149326793,"version":"3.54.6"},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100018693","name":"H2020","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100018693","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003030","name":"Ag\u00e8ncia de Gesti\u00f3 d&apos;Ajuts Universitaris i de Recerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"MICINN","doi-asserted-by":"publisher","award":["PID2022-141529NB-C21"],"award-info":[{"award-number":["PID2022-141529NB-C21"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"MICINN","doi-asserted-by":"publisher","award":["PID2022-139835NB-C21"],"award-info":[{"award-number":["PID2022-139835NB-C21"]}],"id":[{"id":"10.13039\/501100003329","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":[[2026,9]]},"DOI":"10.1016\/j.ijar.2026.109699","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T23:07:44Z","timestamp":1777590464000},"page":"109699","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Non-falsity and general threshold-preserving companions of MTL logics"],"prefix":"10.1016","volume":"196","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8528-369X","authenticated-orcid":false,"given":"Joan","family":"Gispert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6929-3126","authenticated-orcid":false,"given":"Llu\u00eds","family":"Godo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4466-3298","authenticated-orcid":false,"given":"Francesc","family":"Esteva","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.ijar.2026.109699_bib0001","article-title":"Metamathematics of Fuzzy Logic","volume":"4","author":"H\u00e1jek","year":"1998"},{"key":"10.1016\/j.ijar.2026.109699_bib0002","series-title":"Handbook of Mathematical Fuzzy Logic - Volume 1","first-page":"103","article-title":"A general framework for mathematical fuzzy logic","author":"Cintula","year":"2011"},{"issue":"6","key":"10.1016\/j.ijar.2026.109699_bib0003","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1093\/logcom\/exp030","article-title":"Logics preserving degrees of truth from varieties of residuated lattices","volume":"19","author":"Bou","year":"2009","journal-title":"J. Log. Comput."},{"key":"10.1016\/j.ijar.2026.109699_bib0004","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.fss.2014.07.001","article-title":"Paraconsistent fuzzy logic preserving non-falsity","volume":"292","author":"Avron","year":"2016","journal-title":"Fuzzy Set. Syst."},{"issue":"3","key":"10.1016\/j.ijar.2026.109699_bib0005","doi-asserted-by":"crossref","DOI":"10.1093\/jigpal\/jzae126","article-title":"On Nilpotent Minimum logics defined by lattice filters and their paraconsistent non-falsity preserving companions","volume":"33","author":"Gispert","year":"2025","journal-title":"Log. J. IGPL"},{"key":"10.1016\/j.ijar.2026.109699_bib0006","series-title":"Arnon Avron on Semantics and Proof Theory of Non-Classical Logics","first-page":"107","article-title":"Degree-preserving G\u00f6del logics with an involution: intermediate logics and (ideal) paraconsistency","author":"Coniglio","year":"2021"},{"key":"10.1016\/j.ijar.2026.109699_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.fss.2025.109563","article-title":"Filter-induced entailment relations in paraconsistent G\u00f6del logics","volume":"520","author":"Frittella","year":"2025","journal-title":"Fuzzy Set. Syst."},{"key":"10.1016\/j.ijar.2026.109699_bib0008","series-title":"Proceedings of the 20th International Conference of Information Processing and Management of Uncertainty (IPMU 2024)","first-page":"375","article-title":"On the paraconsistent companions of involutive fuzzy logics that preserve non-falsity","volume":"1175","author":"Esteva","year":"2025"},{"key":"10.1016\/j.ijar.2026.109699_bib0009","series-title":"Proceedings of the 13th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2025","first-page":"335","article-title":"On the non-falsity and threshold preserving variants of MTL logics","author":"Esteva","year":"2025"},{"key":"10.1016\/j.ijar.2026.109699_bib0010","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0165-0114(01)00098-7","article-title":"Monoidal t-norm based logic: towards a logic for left-continuous t-norms","volume":"124","author":"Esteva","year":"2001","journal-title":"Fuzzy Set. Syst."},{"issue":"2","key":"10.1016\/j.ijar.2026.109699_bib0011","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1023\/A:1015122331293","article-title":"A proof of standard completeness for Esteva and Godo\u2019s logic MTL","volume":"70","author":"Jenei","year":"2002","journal-title":"Stud. Log."},{"key":"10.1016\/j.ijar.2026.109699_bib0012","article-title":"Algebraizable Logics","volume":"396","author":"Blok","year":"1989"},{"issue":"2","key":"10.1016\/j.ijar.2026.109699_bib0013","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1016548805869","article-title":"On the standard and rational completeness of some axiomatic extensions of the monoidal T-norm logic","volume":"71","author":"Esteva","year":"2002","journal-title":"Stud Log."},{"issue":"3","key":"10.1016\/j.ijar.2026.109699_bib0014","doi-asserted-by":"crossref","first-page":"863","DOI":"10.2178\/jsl\/1154698581","article-title":"On theories and models in fuzzy predicate logics","volume":"71","author":"H\u00e1jek","year":"2006","journal-title":"J. Symb. Log."},{"key":"10.1016\/j.ijar.2026.109699_bib0015","series-title":"Handbook of Mathematical Fuzzy Logic - Volume 1","first-page":"1","article-title":"Introduction to mathematical fuzzy logic","author":"B\u011bhounek","year":"2011"},{"issue":"5","key":"10.1016\/j.ijar.2026.109699_bib0016","first-page":"441","article-title":"T-norm based logics with n-contraction","volume":"12","author":"Ciabattoni","year":"2002","journal-title":"Neural Netw. World"},{"issue":"5","key":"10.1016\/j.ijar.2026.109699_bib0017","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/03081070500033799","article-title":"The structure of n-contractive t-norms","volume":"34","author":"Mesiarov\u00e1","year":"2005","journal-title":"Int. J. Gen. Syst."},{"issue":"6","key":"10.1016\/j.ijar.2026.109699_bib0018","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1093\/jigpal\/jzu016","article-title":"Logics of formal inconsistency arising from systems of fuzzy logic","volume":"22","author":"Coniglio","year":"2014","journal-title":"Log. J. IGPL"},{"key":"10.1016\/j.ijar.2026.109699_bib0019","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s001530050006","article-title":"Residuated fuzzy logics with an involutive negation","volume":"39","author":"Esteva","year":"2000","journal-title":"Arch. Math. Log."},{"key":"10.1016\/j.ijar.2026.109699_bib0020","doi-asserted-by":"crossref","first-page":"3125","DOI":"10.1016\/j.fss.2006.06.016","article-title":"T-norm-based logics with an independent involutive negation","volume":"157","author":"Flaminio","year":"2006","journal-title":"Fuzzy Set. Syst."},{"key":"10.1016\/j.ijar.2026.109699_bib0021","series-title":"Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence (UAI095)","first-page":"149","article-title":"Numerical representation of acceptance","author":"Dubois","year":"1995"},{"key":"10.1016\/j.ijar.2026.109699_bib0022","series-title":"Vagueness and Degrees of Truth","author":"Smith","year":"2008"},{"key":"10.1016\/j.ijar.2026.109699_bib0023","series-title":"Paradoxes between Truth and Proof. Synthese Library","article-title":"Tolerance and degrees of truth","author":"Cobreros","year":"2024"},{"key":"10.1016\/j.ijar.2026.109699_bib0024","series-title":"Proc. of the 40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010","first-page":"83","article-title":"Infinite-valued \u0141ukasiewicz logic based on principal lattice filters","author":"Bou","year":"2010"},{"issue":"3","key":"10.1016\/j.ijar.2026.109699_bib0025","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1093\/jigpal\/jzw006","article-title":"On the set of intermediate logics between truth and degree preserving Lukasiewicz logic","volume":"24","author":"Coniglio","year":"2016","journal-title":"Log. J. IGPL"},{"issue":"2","key":"10.1016\/j.ijar.2026.109699_bib0026","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1093\/logcom\/exi075","article-title":"On product logic with truth-constants","volume":"16","author":"Savick\u00fd","year":"2006","journal-title":"J. Log. Comput."},{"key":"10.1016\/j.ijar.2026.109699_bib0027","series-title":"Handbook of Philosophical Logic","first-page":"115","article-title":"Refutation systems in propositional logic","volume":"16","author":"Skura","year":"2011"},{"key":"10.1016\/j.ijar.2026.109699_bib0028","first-page":"287","article-title":"Paraconsistent Logic","volume":"vol. 6","author":"Priest","year":"2002"},{"key":"10.1016\/j.ijar.2026.109699_bib0029","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1305\/ndjfl\/1093891487","article-title":"On the theory of inconsistent formal systems","volume":"15","author":"da Costa","year":"1974","journal-title":"Notre Dame J. Form. Log."},{"key":"10.1016\/j.ijar.2026.109699_bib0030","article-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","volume":"40","author":"Carnielli","year":"2016"},{"key":"10.1016\/j.ijar.2026.109699_bib0031","series-title":"Proceedings of TABLEAUX\u201999, Analytic Tableaux and Related Methods, LNAI 1617","first-page":"213-128","article-title":"Bounded contraction in systems with linearity","author":"Ciabattoni","year":"1999"}],"container-title":["International Journal of Approximate Reasoning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X26000757?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0888613X26000757?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T06:21:49Z","timestamp":1783146109000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0888613X26000757"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":31,"alternative-id":["S0888613X26000757"],"URL":"https:\/\/doi.org\/10.1016\/j.ijar.2026.109699","relation":{},"ISSN":["0888-613X"],"issn-type":[{"value":"0888-613X","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Non-falsity and general threshold-preserving companions of MTL logics","name":"articletitle","label":"Article Title"},{"value":"International Journal of Approximate Reasoning","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ijar.2026.109699","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"109699"}}