{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T20:32:20Z","timestamp":1768249940592,"version":"3.49.0"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2658,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is well known that classical propositional logic can be interpreted in intuitionistic prepositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part of the paper, we also discuss some extended forms of the Koltnogorov translation and we compare it to the Glivenko translation.<\/jats:p>","DOI":"10.2178\/jsl\/1164060460","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T16:24:03Z","timestamp":1198081443000},"page":"1353-1384","source":"Crossref","is-referenced-by-count":23,"title":["Glivenko theorems for substructural logics over FL"],"prefix":"10.1017","volume":"71","author":[{"given":"Nikolaos","family":"Galatos","sequence":"first","affiliation":[]},{"given":"Hiroakira","family":"Ono","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005818_ref017","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1093\/oso\/9780198537779.003.0010","volume-title":"Substructural Logics","author":"Ono","year":"1993"},{"key":"S0022481200005818_ref014","first-page":"183","article-title":"Sur quelques points de la logique de M. Brouwer","volume":"15","author":"Glivenko","year":"1929","journal-title":"Bulletins de la classe des sciences, Academie Royale de Belgique"},{"key":"S0022481200005818_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8305-5"},{"key":"S0022481200005818_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-004-1870-4"},{"key":"S0022481200005818_ref009","unstructured":"Galatos N. , Varieties of residuated lattices, Ph.D. thesis , Vanderbilt University, 2003."},{"key":"S0022481200005818_ref008","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024621922509"},{"key":"S0022481200005818_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s001530200144"},{"key":"S0022481200005818_ref003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001511"},{"key":"S0022481200005818_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-004-6043-0"},{"key":"S0022481200005818_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.07.002"},{"key":"S0022481200005818_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3"},{"key":"S0022481200005818_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9480-6"},{"key":"S0022481200005818_ref006","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200310082"},{"key":"S0022481200005818_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197181"},{"key":"S0022481200005818_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/0396"},{"key":"S0022481200005818_ref012","unstructured":"Galatos N. and Ono H. , Cut elimination and strong separation for substructural logics: An algebraic approach, manuscript."},{"key":"S0022481200005818_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-003-1822-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005818","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T15:40:53Z","timestamp":1708443653000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005818\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["S0022481200005818"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1164060460","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}