{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:08:20Z","timestamp":1753877300457,"version":"3.41.2"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T00:00:00Z","timestamp":1715731200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this work we present two new classes of logics determined by specific properties of the Leibniz operator that expand the Leibniz hierarchy. By doing so, we present a sufficient condition for the commutativity of the Leibniz operator with inverse substitutions\/homomorphisms, which gives us a negative answer to the possibility of establishing a precise connection between Leibniz classes and the behavior of the Leibniz operator.<\/jats:p>","DOI":"10.1093\/logcom\/exae025","type":"journal-article","created":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T05:31:13Z","timestamp":1715837473000},"source":"Crossref","is-referenced-by-count":0,"title":["Expanding the Leibniz Hierarchy"],"prefix":"10.1093","volume":"35","author":[{"given":"Ugo C M","family":"Almeida","sequence":"first","affiliation":[{"name":"Department of Mathematics , Federal University of Bahia, Av. Milton Santos s\/n, Salvador, 40.170-110, Bahia, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Darllan Concei\u00e7\u00e3o","family":"Pinto","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Federal University of Bahia, Av. Milton Santos s\/n, Salvador, 40.170-110, Bahia, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,5,15]]},"reference":[{"key":"2025061108221930900_ref1","article-title":"Truth-equational logics, full models, and the Frege hierarchy","volume-title":"Don Pigozzi on Abstract Algebraic Logic and Universal Algebra, Outstanding Contributions to Logic","author":"Albuquerque","year":"2018"},{"key":"2025061108221930900_ref2","first-page":"2005","article-title":"Fibring and Sheaves","volume-title":"Proceedings of IICAI-05, Special Session at the 2nd Indian International Conference on Artificial Intelligence","author":"Arndt","year":"1679\u20131698"},{"key":"2025061108221930900_ref3","first-page":"3","article-title":"On the category of algebraizable logics","volume":"1","author":"Arndt","year":"2006","journal-title":"CLE e-Prints"},{"key":"2025061108221930900_ref4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11787-006-0002-7","article-title":"A global glance on categories in Logic","volume":"1","author":"Arndt","year":"2007","journal-title":"Logica Universalis"},{"key":"2025061108221930900_ref5","first-page":"257","article-title":"Finitary filter pairs and propositional logics","volume":"4","author":"Arndt","year":"2018","journal-title":"South American Journal of Logic"},{"key":"2025061108221930900_ref6","article-title":"Congruence filter pairs, adjoints and Leibniz hierarchy","volume-title":"Journal of Logic and Computation","author":"Arndt","year":"2024"},{"key":"2025061108221930900_ref7","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0396","article-title":"Algebraizable logics","volume-title":"Memoirs of the AMS, 396, American Mathematical Society","author":"Blok","year":"1989"},{"key":"2025061108221930900_ref8","article-title":"Handbook of Categorical Algebra: Volume 1, Basic Category Theory","volume-title":"Encyclopedia of Mathematics and Its Applications","author":"Borceux","year":"1994"},{"key":"2025061108221930900_ref9","article-title":"Protoalgebraic logics","volume-title":"Trends in Logic - Studia Logica Library, v. 10","author":"Czelakowski","year":"2001"},{"volume-title":"Abstract Algebraic Logic - An Introductory Textbook","year":"2016.","author":"Font","key":"2025061108221930900_ref10"},{"volume-title":"Protoalgebraic and Equivalential Logics","year":"2016","author":"Hakoniemi","key":"2025061108221930900_ref11"},{"key":"2025061108221930900_ref12","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1017\/jsl.2021.48","article-title":"The poset of all logics I: interpretations and lattice structure","volume":"86","author":"Jansana","year":"2021","journal-title":"Journal of Symbolic Logic"},{"issue":"1","key":"2025061108221930900_ref13","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1017\/jsl.2021.49","article-title":"The poset of all logics II: Leibniz classes and hierarchy","volume":"88","author":"Jansana","year":"2021","journal-title":"Published online in the Journal of Symbolic Logic"},{"key":"2025061108221930900_ref14","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1007\/s11225-020-09916-z","article-title":"The poset of all logics III: Finitely presentable logics","volume":"109","author":"Jansana","year":"2021","journal-title":"Studia Logica"},{"key":"2025061108221930900_ref15","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0022-4049(93)90171-O","article-title":"Factorization systems as Eilenberg-Moore algebras","volume":"85","author":"Korostenski","year":"1993","journal-title":"Journal of Pure and Applied Algebra"},{"key":"2025061108221930900_ref16","first-page":"407","article-title":"Analyzing categories of signatures","volume":"4","author":"Mariano","year":"2018","journal-title":"South American Journal of Logic"},{"key":"2025061108221930900_ref17","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1093\/jigpal\/jzx014","article-title":"Algebraizable Logics and a functorial encoding of its morphisms","volume":"25","author":"Mariano","year":"2017","journal-title":"Logic Journal of the IGPL"},{"key":"2025061108221930900_ref18","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1016\/j.apal.2019.02.003","article-title":"On the complexity of the Leibniz Hierarchy","volume":"170","author":"Moraschini","year":"2019","journal-title":"Annals of Pure and Applied Logic"},{"key":"2025061108221930900_ref19","first-page":"95","article-title":"The equational definability of truth predicates","volume":"41","author":"Raftery","year":"2006","journal-title":"Reports on Mathematical Logic"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/5\/exae025\/57687361\/exae025.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/5\/exae025\/57687361\/exae025.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T12:22:29Z","timestamp":1749644549000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/doi\/10.1093\/logcom\/exae025\/7673389"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,15]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,6,11]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exae025","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2025,7]]},"published":{"date-parts":[[2024,5,15]]},"article-number":"exae025"}}