{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T11:44:09Z","timestamp":1781869449357,"version":"3.54.5"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T00:00:00Z","timestamp":1736812800000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,5,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Nilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov\u2019s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, with special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains.<\/jats:p>","DOI":"10.1093\/jigpal\/jzae126","type":"journal-article","created":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T13:48:12Z","timestamp":1736862492000},"source":"Crossref","is-referenced-by-count":4,"title":["On Nilpotent Minimum logics defined by lattice filters and their paraconsistent non-falsity preserving companions"],"prefix":"10.1093","volume":"33","author":[{"given":"Joan","family":"Gispert","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona , 08007 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesc","family":"Esteva","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Research Institute (IIIA)\u2013CSIC , 08193 Bellaterra, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Llu\u00eds","family":"Godo","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Research Institute (IIIA)\u2013CSIC , 08193 Bellaterra, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcelo E","family":"Coniglio","sequence":"additional","affiliation":[{"name":"Centre for Logic, Epistemology and the History of Science (CLE), and Institute of Philosophy and the Humanities (IFCH), University of Campinas (UNICAMP) , 13083-859 Campinas, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,1,13]]},"reference":[{"key":"2025052605514438700_ref1","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s11225-011-9346-y","article-title":"Ideal paraconsistent logics","volume":"99","author":"Arieli","year":"2011","journal-title":"Stud Log"},{"key":"2025052605514438700_ref2","doi-asserted-by":"publisher","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 Sets Syst"},{"key":"2025052605514438700_ref3","article-title":"Abstract algebraic logic and the deduction theorem","author":"Blok","year":"2001"},{"key":"2025052605514438700_ref4","doi-asserted-by":"publisher","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":"2025052605514438700_ref5","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1093\/logcom\/exn081","article-title":"Constructive logic with strong negation as a substructural logic","volume":"20","author":"Busaniche","year":"2010","journal-title":"J Log Comput"},{"key":"2025052605514438700_ref6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4020-6324-4_1","article-title":"Logics of Formal Inconsistency","volume-title":"Handbook of Philosophical Logic","author":"Carnielli","year":"2007"},{"key":"2025052605514438700_ref7","volume-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","author":"Carnielli","year":"2016"},{"key":"2025052605514438700_ref8","first-page":"103","article-title":"A general framework for mathematical fuzzy logic","volume-title":"Handbook of Mathematical Fuzzy Logic\u2014Volume 1","author":"Cintula","year":"2011"},{"key":"2025052605514438700_ref9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-85675-5","volume-title":"Logic and Implication: An Introduction to the General Algebraic Study of Non-Classical Logics","author":"Cintula","year":"2021"},{"key":"2025052605514438700_ref10","doi-asserted-by":"publisher","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":"2025052605514438700_ref11","doi-asserted-by":"publisher","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"},{"key":"2025052605514438700_ref12","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1093\/logcom\/exy032","article-title":"Maximality in finite-valued Lukasiewicz Logics defined by order filters","volume":"29","author":"Coniglio","year":"2019","journal-title":"J Log Comput"},{"key":"2025052605514438700_ref13","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/978-3-030-71258-7_6","article-title":"Degree-preserving G\u00f6del logics with an involution: intermediate logics and (ideal) paraconsistency","volume-title":"Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. 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