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Using rexpansions, a semantic method for obtaining conservative extensions of (N)matrix-defined logics is introduced and applied to fragments of the classical two-valued matrix, as well as to other many-valued matrices and Nmatrices. The main application of this method is the construction and investigation of truth-preserving \u00ac-paraconsistent conservative extensions of G\u00f6del fuzzy logic, in which \u00ac has several desired properties. This is followed by some results regarding the relations between the constructed logics.<\/jats:p>","DOI":"10.1017\/s1755020318000321","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T09:32:06Z","timestamp":1540546326000},"page":"173-200","source":"Crossref","is-referenced-by-count":12,"title":["REXPANSIONS OF NONDETERMINISTIC MATRICES AND THEIR APPLICATIONS IN NONCLASSICAL LOGICS"],"prefix":"10.1017","volume":"12","author":[{"given":"ARNON","family":"AVRON","sequence":"first","affiliation":[]},{"given":"YONI","family":"ZOHAR","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,10,26]]},"reference":[{"key":"S1755020318000321_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/BF00258428"},{"key":"S1755020318000321_ref24","first-page":"51","article-title":"Philosophische bemerkungen zu mehrwertigen systemen der aussagenlogik","author":"\u0141ukasiewicz","year":"1930","journal-title":"Comptes Rendus de la Siciete des Sciences et des Letters de Varsovie"},{"key":"S1755020318000321_ref23","first-page":"575","article-title":"Studying sequent systems via non-deterministic multiple-valued matrices","volume":"9","author":"Lahav","year":"2013","journal-title":"International Symposium on Multiple-Valued Logic"},{"key":"S1755020318000321_ref22","first-page":"53","volume-title":"Trivalent Logics and their Applications, Proceedings of ESSLLI 2012 Workshop","author":"Kulicki","year":"2012"},{"key":"S1755020318000321_ref21","doi-asserted-by":"publisher","DOI":"10.2307\/2267778"},{"key":"S1755020318000321_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1489-0"},{"key":"S1755020318000321_ref18","first-page":"1","volume-title":"Handbook of Philosophical Logic","volume":"6","author":"Dunn","year":"2002"},{"key":"S1755020318000321_ref15","first-page":"1","volume-title":"Handbook of Philosophical Logic, Second Edition","volume":"14","author":"Carnielli","year":"2007"},{"key":"S1755020318000321_ref13","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exp030"},{"key":"S1755020318000321_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2017.16"},{"key":"S1755020318000321_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0479-4_4"},{"key":"S1755020318000321_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exi001"},{"key":"S1755020318000321_ref9","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2012.20"},{"key":"S1755020318000321_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-29300-4_2"},{"key":"S1755020318000321_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2006.06.011"},{"key":"S1755020318000321_ref6","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093636612"},{"key":"S1755020318000321_ref5","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093958482"},{"key":"S1755020318000321_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-010-9296-9"},{"key":"S1755020318000321_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-81-322-2719-9_4"},{"key":"S1755020318000321_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(98)00032-0"},{"key":"S1755020318000321_ref1","volume-title":"Entailment: The Logic of Relevance and Necessity","volume":"I","author":"Anderson","year":"1975"},{"key":"S1755020318000321_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jal.2004.07.017"},{"key":"S1755020318000321_ref16","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093891487"},{"key":"S1755020318000321_ref28","unstructured":"Zohar Y. 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Gentzen-type Proof Systems for Non-classical Logics, Ph.D. Thesis, Tel Aviv University."},{"key":"S1755020318000321_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/2964753"},{"key":"S1755020318000321_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0452-6_4"},{"key":"S1755020318000321_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3"},{"key":"S1755020318000321_ref14","doi-asserted-by":"publisher","DOI":"10.1201\/9780203910139"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020318000321","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T19:00:58Z","timestamp":1555095658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020318000321\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,26]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["S1755020318000321"],"URL":"https:\/\/doi.org\/10.1017\/s1755020318000321","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,26]]}}}