{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T23:20:21Z","timestamp":1772580021272,"version":"3.50.1"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"unspecified","delay-in-days":71,"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":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The variety of quasi-Nelson algebras (QNAs) has been recently introduced and characterised in several equivalent ways: among others, as (1) the class of bounded commutative integral (but non-necessarily involutive) residuated lattices satisfying the Nelson identity, as well as (2) the class of (0, 1)-congruence orderable commutative integral residuated lattices. Logically, QNAs are the algebraic counterpart of quasi-Nelson logic, which is the (algebraisable) extension of the substructural logic \u2131\u2112<jats:italic><jats:sub>ew<\/jats:sub><\/jats:italic> (Full Lambek calculus with Exchange and Weakening) by the Nelson axiom. In the present paper, we collect virtually all the results that are currently known on QNAs, including solutions to certain questions left open in earlier publications. Furthermore, we extend our study to some subreducts of QNAs, that is, classes of algebras corresponding to fragments of the algebraic language obtained by eliding either the implication or the lattice operations.<\/jats:p>","DOI":"10.1017\/s0960129521000049","type":"journal-article","created":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T07:10:27Z","timestamp":1620717027000},"page":"257-285","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":9,"title":["Quasi-Nelson algebras and fragments"],"prefix":"10.1017","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1364-5003","authenticated-orcid":false,"given":"Umberto","family":"Rivieccio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ramon","family":"Jansana","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,5,11]]},"reference":[{"key":"S0960129521000049_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00098-7"},{"key":"S0960129521000049_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-008-9138-1"},{"key":"S0960129521000049_ref15","first-page":"499","article-title":"Fragments of quasi-Nelson: two negations","volume":"7","author":"Rivieccio","year":"2020","journal-title":"Journal of Applied Logic"},{"key":"S0960129521000049_ref6","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics","author":"Galatos","year":"2007"},{"key":"S0960129521000049_ref11","doi-asserted-by":"publisher","DOI":"10.2307\/2268973"},{"key":"S0960129521000049_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-014-0272-5"},{"key":"S0960129521000049_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-50153-2_47"},{"key":"S0960129521000049_ref22","first-page":"13","article-title":"Topologicality of Kleene algebras with a weak pseudocomplementation over distributive p-algebras","volume":"25","author":"Sendlewski","year":"1991","journal-title":"Reports on Mathematical Logic"},{"key":"S0960129521000049_ref7","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.2000.8622"},{"key":"S0960129521000049_ref12","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/13.4.453"},{"key":"S0960129521000049_ref21","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200029716"},{"key":"S0960129521000049_ref1","volume-title":"Distributive Lattices","author":"Balbes","year":"1974"},{"key":"S0960129521000049_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0396"},{"key":"S0960129521000049_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01195727"},{"key":"S0960129521000049_ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-008-9113-x"},{"key":"S0960129521000049_ref20","first-page":"133","volume-title":"Algebraic Perspectives on Substructural Logics (Trends in Logic 55)","author":"Rivieccio","year":"2020"},{"key":"S0960129521000049_ref13","volume-title":"An Algebraic Approach to Non-classical Logics","author":"Rasiowa","year":"1974"},{"key":"S0960129521000049_ref9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196709005251"},{"key":"S0960129521000049_ref4","doi-asserted-by":"publisher","DOI":"10.2478\/s11533-009-0032-5"},{"key":"S0960129521000049_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-020-04885-w"},{"key":"S0960129521000049_ref17","doi-asserted-by":"crossref","unstructured":"Rivieccio, U. , Flaminio, T. and Nascimento, T. (2020a). On the representation of (weak) nilpotent minimum algebras. In: 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE, Glasgow, United Kingdom, 2020), 1\u20138, doi: 10.1109\/FUZZ48607.2020.9177641.","DOI":"10.1109\/FUZZ48607.2020.9177641"},{"key":"S0960129521000049_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-59533-6_27"},{"key":"S0960129521000049_ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-3588-9"},{"key":"S0960129521000049_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2019.07.011"},{"key":"S0960129521000049_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7633-9"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129521000049","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T13:14:42Z","timestamp":1640006082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129521000049\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["S0960129521000049"],"URL":"https:\/\/doi.org\/10.1017\/s0960129521000049","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. 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