{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T16:54:09Z","timestamp":1773334449920,"version":"3.50.1"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T00:00:00Z","timestamp":1543449600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A recent paper by Jakl, Jung and Pultr (2016, Electron. Notes Theor. Comput. Sci., 325, 201\u2013219) succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices (the algebraic counterpart of Nelson\u2019s paraconsistent logic) to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability (and some non-algebraizability) results for the corresponding logics.<\/jats:p>","DOI":"10.1093\/jigpal\/jzy070","type":"journal-article","created":{"date-parts":[[2018,10,17]],"date-time":"2018-10-17T18:04:09Z","timestamp":1539799449000},"page":"973-999","source":"Crossref","is-referenced-by-count":8,"title":["Non-involutive twist-structures"],"prefix":"10.1093","volume":"28","author":[{"given":"Umberto","family":"Rivieccio","sequence":"first","affiliation":[{"name":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, UFRN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paulo","family":"Maia","sequence":"additional","affiliation":[{"name":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Matem\u00e1tica Aplicada e Estat\u00edstica, UFRN, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Achim","family":"Jung","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Birmingham, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,11,29]]},"reference":[{"key":"2020092508543649500_ref1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.2307\/2274105","article-title":"Constructible falsity and inexact predicates","volume":"49","author":"Almukdad","year":"1984","journal-title":"The Journal of Symbolic Logic"},{"key":"2020092508543649500_ref2","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF00215626","article-title":"Reasoning with logical bilattices","volume":"5","author":"Arieli","year":"1996","journal-title":"Journal of Logic, Language and Information"},{"key":"2020092508543649500_ref3","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0396","volume-title":"Algebraizable Logics","author":"Blok","year":"1989"},{"key":"2020092508543649500_ref4","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s00012-011-0151-2","article-title":"Varieties of interlaced bilattices","volume":"66","author":"Bou","year":"2011","journal-title":"Algebra Universalis"},{"key":"2020092508543649500_ref5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1093\/jigpal\/jzq041","article-title":"The logic of distributive bilattices","volume":"19","author":"Bou","year":"2011","journal-title":"Logic Journal of the IGPL"},{"key":"2020092508543649500_ref6","volume-title":"A Course in Universal Algebra","author":"Burris","year":"2000"},{"key":"2020092508543649500_ref7","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2807-2","volume-title":"Protoalgebraic Logics,","author":"Czelakowski","year":"2001"},{"key":"2020092508543649500_ref8","article-title":"A general algebraic semantics for sentential logics. In Lecture Notes in Logic","author":"Font","year":"2009"},{"key":"2020092508543649500_ref9","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1111\/j.1467-8640.1988.tb00280.x","article-title":"Multivalued logics: a uniform approach to inference in artificial intelligence","volume":"4","author":"Ginsberg","year":"1988","journal-title":"Computational Intelligence"},{"key":"2020092508543649500_ref10","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.entcs.2016.09.039","article-title":"Bitopology and four-valued logic","volume":"325","author":"Jakl","year":"2016","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"2020092508543649500_ref11","article-title":"On the bitopological nature of Stone duality","author":"Jung","year":"2006"},{"key":"2020092508543649500_ref12","first-page":"53","article-title":"Non-involutive bilattices","volume-title":"Anais da Escola de Inform\u00e1tica Te\u00f3rica e M\u00e9todos Formais (ETMF 2016), Natal (Brazil), 22\u201323 November 2016","author":"Maia","year":"2016"},{"key":"2020092508543649500_ref13","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1093\/logcom\/13.4.453","article-title":"Algebraic semantics for paraconsistent Nelson\u2019s logic","volume":"13","author":"Odintsov","year":"2003","journal-title":"Journal of Logic and Computation"},{"key":"2020092508543649500_ref14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-6867-6","volume-title":"Constructive Negations and Paraconsistency","author":"Odintsov","year":"2008"},{"key":"2020092508543649500_ref15","first-page":"95","article-title":"The equational definability of truth predicates","volume":"41","author":"Raftery","year":"2006","journal-title":"Reports on Mathematical Logic"},{"key":"2020092508543649500_ref16","volume-title":"An algebraic approach to non-classical logics. InStudies in Logic and the Foundations of Mathematics","author":"Rasiowa","year":"1974"},{"key":"2020092508543649500_ref17","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s00012-014-0272-5","article-title":"Implicative twist-structures","volume":"71","author":"Rivieccio","year":"2014","journal-title":"Algebra Universalis"},{"key":"2020092508543649500_ref18","first-page":"155","article-title":"Four-valued modal logic: Kripke semantics and duality","volume-title":"Journal of Logic and Computation","author":"Rivieccio","year":"2017"},{"key":"2020092508543649500_ref19","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-6942-2","volume-title":"Theory of Logical Calculi. Basic Theory of Consequence Operations","author":"W\u00f3jcicki","year":"1988"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/jigpal\/article-pdf\/28\/5\/973\/33791670\/jzy070.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/jigpal\/article-pdf\/28\/5\/973\/33791670\/jzy070.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T08:55:21Z","timestamp":1601024121000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/28\/5\/973\/5173466"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,29]]},"references-count":19,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,11,29]]},"published-print":{"date-parts":[[2020,9,25]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzy070","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,10]]},"published":{"date-parts":[[2018,11,29]]}}}