{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,25]],"date-time":"2024-05-25T00:12:46Z","timestamp":1716595966650},"reference-count":51,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T00:00:00Z","timestamp":1623283200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,9]]},"abstract":"Abstract<\/jats:title>A notion of interpretation between arbitrary logics is introduced, and the poset$\\mathsf {Log}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>of all logics ordered under interpretability is studied. It is shown that in$\\mathsf {Log}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between$\\mathsf {Log}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and the lattice of interpretability types of varieties are investigated.<\/jats:p>","DOI":"10.1017\/jsl.2021.48","type":"journal-article","created":{"date-parts":[[2021,6,10]],"date-time":"2021-06-10T10:56:37Z","timestamp":1623322597000},"page":"935-964","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["THE POSET OF ALL LOGICS I: INTERPRETATIONS AND LATTICE STRUCTURE"],"prefix":"10.1017","volume":"86","author":[{"given":"R.","family":"JANSANA","sequence":"first","affiliation":[]},{"given":"T.","family":"MORASCHINI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,6,10]]},"reference":[{"key":"S0022481221000487_r46","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-3671151"},{"key":"S0022481221000487_r48","doi-asserted-by":"publisher","DOI":"10.1007\/BF02485261"},{"key":"S0022481221000487_r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2807-2"},{"key":"S0022481221000487_r14","first-page":"1242","article-title":"Some characterization theorems for infinitary universal Horn logic without equality","volume":"61","author":"Dellunde","year":"1996","journal-title":"this Journal"},{"key":"S0022481221000487_r21","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80086-2"},{"key":"S0022481221000487_r12","first-page":"641","article-title":"Weakly algebraizable logics","volume":"65","author":"Czelakowski","year":"2000","journal-title":"this Journal"},{"key":"S0022481221000487_r24","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004979825733"},{"key":"S0022481221000487_r42","first-page":"1","article-title":"Constructing natural extensions of propositional logics","volume":"82","author":"P\u0159enosil","year":"2015","journal-title":"Studia Logica"},{"key":"S0022481221000487_r33","first-page":"211","volume-title":"Logic and Algebra","volume":"180","author":"McKenzie","year":"1996"},{"key":"S0022481221000487_r16","doi-asserted-by":"crossref","DOI":"10.1017\/9781316716915","volume-title":"A General Algebraic Semantics for Sentential Logics","volume":"7","author":"Font","year":"2017"},{"key":"S0022481221000487_r29","volume-title":"Memoirs of the American Mathematical Society","volume":"222","author":"Kearnes","year":"2013"},{"key":"S0022481221000487_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2019.02.003"},{"key":"S0022481221000487_r30","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.50.5.869"},{"key":"S0022481221000487_r51","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-6942-2"},{"key":"S0022481221000487_r5","volume-title":"Memoirs of the American Mathematical Society","author":"Blok","year":"1989"},{"key":"S0022481221000487_r2","first-page":"277","article-title":"A model theoretic approach to Malcev conditions","volume":"42","author":"Baldwin","year":"1977","journal-title":"this Journal"},{"key":"S0022481221000487_r32","first-page":"13","article-title":"Modal equivalential logics","volume":"3","author":"Malinowski","year":"1986","journal-title":"Journal of Non-Classical Logic"},{"key":"S0022481221000487_r8","doi-asserted-by":"publisher","DOI":"10.1007\/BF00373095"},{"key":"S0022481221000487_r31","first-page":"3","article-title":"On the general theory of algebraic system","volume":"77","author":"Mal\u2019cev","year":"1954","journal-title":"Matematicheskii Sbornik"},{"key":"S0022481221000487_r38","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-019-0611-7"},{"key":"S0022481221000487_r3","doi-asserted-by":"publisher","DOI":"10.1201\/9781439851302"},{"key":"S0022481221000487_r13","first-page":"101","volume-title":"Contributions to Lattice Theory (Szeged, 1980)","author":"Davey","year":"1983"},{"key":"S0022481221000487_r43","first-page":"903","article-title":"Correspondences between Gentzen and Hilbert systems","volume":"71","author":"Raftery","year":"2006","journal-title":"this Journal"},{"key":"S0022481221000487_r28","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-020-09916-z"},{"key":"S0022481221000487_r23","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370843"},{"key":"S0022481221000487_r20","volume-title":"The Lattice of Interpretability Types of Varieties","volume":"50","author":"Garc\u00eda","year":"1984"},{"key":"S0022481221000487_r35","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2018.47"},{"key":"S0022481221000487_r1","volume-title":"Don Pigozzi on Abstract Algebraic Logic and Universal Algebra,","author":"Albuquerque","year":"2018"},{"key":"S0022481221000487_r47","doi-asserted-by":"publisher","DOI":"10.1007\/BF02945141"},{"key":"S0022481221000487_r26","unstructured":"[26] Jansana, R. and Moraschini, T. , Relational semantics and ordered algebras for deductive systems, Manuscript, 2021."},{"key":"S0022481221000487_r11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024678007488"},{"key":"S0022481221000487_r9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02584057"},{"key":"S0022481221000487_r18","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzu003"},{"key":"S0022481221000487_r6","first-page":"1","volume-title":"Universal Algebra and Quasigroup Theory","author":"Blok","year":"1992"},{"key":"S0022481221000487_r27","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2021.49"},{"key":"S0022481221000487_r17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024621922509"},{"key":"S0022481221000487_r49","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1977-054-9"},{"key":"S0022481221000487_r15","volume-title":"Abstract Algebraic Logic - An Introductory Textbook","volume":"60","author":"Font","year":"2016"},{"key":"S0022481221000487_r39","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700017122"},{"key":"S0022481221000487_r50","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060213"},{"key":"S0022481221000487_r34","first-page":"83","article-title":"On everywhere strongly logifiable algebras","volume":"50","author":"Moraschini","year":"2015","journal-title":"Reports on Mathematical Logic"},{"key":"S0022481221000487_r7","unstructured":"[7] Burris, S. and Sankappanavar, H. P. , A course in universal algebra, 2012, The millennium edition. Available at https:\/\/www.math.uwaterloo.ca\/~snburris\/htdocs\/ualg.html."},{"key":"S0022481221000487_r25","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/076"},{"key":"S0022481221000487_r19","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-014-0300-5"},{"key":"S0022481221000487_r36","doi-asserted-by":"publisher","DOI":"10.1017\/S175502031800014X"},{"key":"S0022481221000487_r44","first-page":"95","article-title":"The equational definability of truth predicates","volume":"41","author":"Raftery","year":"2006","journal-title":"Reports on Mathematical Logic"},{"key":"S0022481221000487_r41","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1972-098-8"},{"key":"S0022481221000487_r4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370269"},{"key":"S0022481221000487_r45","doi-asserted-by":"publisher","DOI":"10.2989\/16073606.2011.622856"},{"key":"S0022481221000487_r22","first-page":"85","article-title":"Algebraizability and Beth\u2019s theorem for equivalential logics","volume":"22","author":"Herrmann","year":"1993","journal-title":"Bulletin of the Section of Logic"},{"key":"S0022481221000487_r40","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700005899"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481221000487","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T15:22:26Z","timestamp":1672413746000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481221000487\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,10]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["S0022481221000487"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2021.48","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,10]]},"assertion":[{"value":"\u00a9 Association for Symbolic Logic 2021","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}