{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T22:42:00Z","timestamp":1700174520453},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5490,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic <jats:bold>RM<\/jats:bold> or with the extensions of <jats:bold>RM<\/jats:bold> and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if <jats:italic>C<\/jats:italic> is a consequence operation with <jats:italic>C<\/jats:italic><jats:sub>RM<\/jats:sub> \u2264 <jats:italic>C<\/jats:italic> and <jats:italic>C<\/jats:italic> admits a deduction theorem scheme, then <jats:italic>C<\/jats:italic> is equal to a consequence operation specified in [13]. In algebraic terms, this means that the only quasivarieties of Sugihara algebras with the relative congruence extension property are the quasivarieties corresponding, via the algebraization process, to the consequence operations specified in [13].<\/jats:p>","DOI":"10.2307\/2586764","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:25Z","timestamp":1146938545000},"page":"279-290","source":"Crossref","is-referenced-by-count":5,"title":["Deduction theorems within RM and its extensions"],"prefix":"10.1017","volume":"64","author":[{"given":"J.","family":"Czelakowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"W.","family":"Dziobiak","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200014031_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02125917"},{"key":"S0022481200014031_ref004","unstructured":"Blok W.J. and Pigozzi D. , The deduction theorem in algebraic logic, to appear."},{"key":"S0022481200014031_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370436"},{"key":"S0022481200014031_ref005","volume-title":"Algebraizable logics","volume":"77","author":"Blok","year":"1989"},{"key":"S0022481200014031_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-6942-2"},{"key":"S0022481200014031_ref002","first-page":"144","volume":"25","author":"Belnap","year":"1960","journal-title":"Entailment and relevance"},{"key":"S0022481200014031_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370271"},{"key":"S0022481200014031_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375898"},{"key":"S0022481200014031_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370679"},{"key":"S0022481200014031_ref001","volume-title":"Entailment: The logic of relevance, vol. I","author":"Anderson","year":"1975"},{"key":"S0022481200014031_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197181"},{"key":"S0022481200014031_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370428"},{"key":"S0022481200014031_ref010","first-page":"1","volume":"35","author":"Dunn","year":"1970","journal-title":"Algebraic completeness results for R-mingle and its extensions"},{"key":"S0022481200014031_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-85796-5"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200014031","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T19:07:30Z","timestamp":1557515250000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200014031\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,3]]}},"alternative-id":["S0022481200014031"],"URL":"https:\/\/doi.org\/10.2307\/2586764","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,3]]}}}