{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T02:57:30Z","timestamp":1648868250520},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,7,23]],"date-time":"2010-07-23T00:00:00Z","timestamp":1279843200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>As is known, a logic S is <jats:italic>paraconsistent<\/jats:italic> if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis\u2019 modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the \u201cLewis\u2019 proof\u201d or \u201cLewis\u2019 argument.\u201d This proof essentially leans on the Disjunctive Syllogism as a <jats:italic>rule of inference<\/jats:italic>. The aim of this paper is to define a series of paraconsistent logics included in S4 where the Disjunctive Syllogism is valid only as a <jats:italic>rule of proof<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s1755020310000109","type":"journal-article","created":{"date-parts":[[2010,7,23]],"date-time":"2010-07-23T09:47:18Z","timestamp":1279878438000},"page":"442-466","source":"Crossref","is-referenced-by-count":0,"title":["PARACONSISTENT LOGICS INCLUDED IN LEWIS\u2019 S4"],"prefix":"10.1017","volume":"3","author":[{"given":"GEMMA","family":"ROBLES","sequence":"first","affiliation":[]},{"given":"JOS\u00c9 M.","family":"M\u00c9NDEZ","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,7,23]]},"reference":[{"key":"S1755020310000109_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10849-009-9085-x"},{"key":"S1755020310000109_ref12","volume-title":"Relevant Logics and their Rivals, Vol. 1","author":"Routley","year":"1982"},{"key":"S1755020310000109_ref8","volume-title":"The Standford Encyclopedia of Philosophy","author":"Priest","year":"2004"},{"key":"S1755020310000109_ref13","volume-title":"Relevant Logics and their Rivals, Vol. 1","author":"Routley","year":"1982"},{"key":"S1755020310000109_ref3","volume-title":"Entailment. The Logic of Relevance and Necessity, Vol II","author":"Anderson","year":"1992"},{"key":"S1755020310000109_ref1","doi-asserted-by":"publisher","DOI":"10.2307\/2268750"},{"key":"S1755020310000109_ref2","volume-title":"Entailment. The Logic of Relevance and Necessity, Vol I","author":"Anderson","year":"1975"},{"key":"S1755020310000109_ref5","volume-title":"Symbolic Logic","author":"Lewis","year":"1932"},{"key":"S1755020310000109_ref6","first-page":"15","article-title":"Exhaustively axiomatizing S3- > and S4- > with a select list of representative theses","volume":"17","author":"M\u00e9ndez","year":"1988","journal-title":"Bulletin of the Section of Logic"},{"key":"S1755020310000109_ref7","first-page":"407","article-title":"Algebraic analysis of entailment I","volume":"15","author":"Meyer","year":"1972","journal-title":"Logique et Analyse"},{"key":"S1755020310000109_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s10849-007-9042-5"},{"key":"S1755020310000109_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF00650498"},{"key":"S1755020310000109_ref14","volume-title":"MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide","author":"Slaney","year":"1995"},{"key":"S1755020310000109_ref4","doi-asserted-by":"publisher","DOI":"10.2307\/2271336"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020310000109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T21:42:53Z","timestamp":1556401373000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020310000109\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,23]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S1755020310000109"],"URL":"https:\/\/doi.org\/10.1017\/s1755020310000109","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,23]]}}}