{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:43:29Z","timestamp":1774953809799,"version":"3.50.1"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1653,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be denned syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. J\u00f3nsson in [3]. Other authors have extended this result to the cases of<jats:italic>\u03ba<\/jats:italic>-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature.<\/jats:p>","DOI":"10.2178\/jsl\/1245158085","type":"journal-article","created":{"date-parts":[[2009,6,16]],"date-time":"2009-06-16T13:16:09Z","timestamp":1245158169000},"page":"780-810","source":"Crossref","is-referenced-by-count":26,"title":["Equivalence of consequence relations: an order-theoretic and categorical perspective"],"prefix":"10.1017","volume":"74","author":[{"given":"Nikolaos","family":"Galatos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Constantine","family":"Tsinakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200003303_ref002","volume-title":"Lattice theory","volume":"XXV","author":"Birkhoff","year":"1967"},{"key":"S0022481200003303_ref014","first-page":"903","volume":"71","author":"Raftery","year":"2006","journal-title":"Correspondences between Gentzen and Hilbert systems"},{"key":"S0022481200003303_ref015","doi-asserted-by":"crossref","first-page":"319","DOI":"10.3233\/FI-1993-182-417","article-title":"On the algebraization of some Gentzen systems","volume":"18","author":"Rebagliato","year":"1993","journal-title":"Fundamenta Informaticae"},{"key":"S0022481200003303_ref009","volume-title":"Residuated lattices: an algebraic glimpse at substructural logics","volume":"151","author":"Galatos","year":"2007"},{"key":"S0022481200003303_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3627-4_3"},{"key":"S0022481200003303_ref007","volume-title":"Many-valued logics 2: Automated reasoning and practical applications","author":"Bolc","year":"2004"},{"key":"S0022481200003303_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(98)00058-X"},{"key":"S0022481200003303_ref005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001511"},{"key":"S0022481200003303_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0396"},{"key":"S0022481200003303_ref001","first-page":"1","volume-title":"Logic: From foundations to applications","author":"Avron","year":"1996"},{"key":"S0022481200003303_ref006","volume-title":"Lattices and ordered algebraic structures","author":"Blyth","year":"2005"},{"key":"S0022481200003303_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8305-5"},{"key":"S0022481200003303_ref011","volume-title":"Annals of Pure and Applied Logic","author":"Galatos"},{"key":"S0022481200003303_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-004-1870-4"},{"key":"S0022481200003303_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8299-z"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200003303","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,7]],"date-time":"2021-10-07T11:37:34Z","timestamp":1633606654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200003303\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S0022481200003303"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1245158085","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}