{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:29:58Z","timestamp":1675211398253},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6493,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,6]]},"abstract":"<jats:p>The history of the Gentzenization of relevant logics goes back to Kripke [17], who in 1959 Gentzenized R<jats:sub>\u2192<\/jats:sub> and went on to prove its decidability. Formulae were separated by commas on the left side of the turnstile, the commas just representing nested implications. Kripke employed just a singleton formula to the right of the turnstile. He also considered adding negation, as well as other connectives, but it was not until 1961 that Belnap and Wallace, in [5], Gentzenized <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200017333_inline1\" \/> and proved its decidability, though their Gentzenization employed commas on both sides of the turnstile. Subsequently, in 1966, the logic R without distribution, now called LR (for lattice R), was Gentzenized in a similar style by Meyer in [20]. He also went on to show decidability for LR by extending Kripke's argument. Later, in 1969, Dunn Gentzenized R<jats:sub>+<\/jats:sub> (published in [1], pp. 381\u2013391) using two structural connectives (commas and semicolons) to the left of the turnstile, and with a single formula to the right. Here, the commas represent conjunction and the semicolons represent an intensional conjunction, called \u201cfusion\u201d. This is all nicely set out in McRobbie [19], where he also introduces left-handed Gentzenizations and analytic tableaux for a number of fragments of relevant logics. In 1979, further work on distributionless logic was done by Grishin, in a series of papers, including [16], in which he produced a Gentzenization of quantified RW without distribution (which we will call LRWQ), and used it to prove the decidability of this quantified logic.<\/jats:p>","DOI":"10.2307\/2275666","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:58:29Z","timestamp":1146941909000},"page":"353-378","source":"Crossref","is-referenced-by-count":7,"title":["Gentzenizations of relevant logics without distribution. I"],"prefix":"10.1017","volume":"61","author":[{"given":"Ross T.","family":"Brady","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017333_ref001","volume-title":"Entailment: the logic of relevance and necessity","volume":"1","author":"Anderson","year":"1975"},{"key":"S0022481200017333_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249365"},{"key":"S0022481200017333_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF00454743"},{"key":"S0022481200017333_ref021","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093887722"},{"key":"S0022481200017333_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF00284976"},{"key":"S0022481200017333_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90037-0"},{"key":"S0022481200017333_ref017","first-page":"324","volume":"24","author":"Kripke","year":"1959","journal-title":"The problem of entailment"},{"key":"S0022481200017333_ref022","first-page":"169","volume":"50","author":"Ono","year":"1985","journal-title":"Logics without the contraction rule"},{"key":"S0022481200017333_ref016","first-page":"316","volume-title":"Studies in nonclassical logics andset theory","author":"Grishin","year":"1979"},{"key":"S0022481200017333_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"S0022481200017333_ref019","unstructured":"McRobbie M. 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K. , Topics in modal and many-valued logic, Ph.D. Thesis , University of Pittsburgh, Pittsburgh, Pennsylvania, 1966."},{"key":"S0022481200017333_ref025","doi-asserted-by":"publisher","DOI":"10.1080\/00048409012340183"},{"key":"S0022481200017333_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF00260741"},{"key":"S0022481200017333_ref006","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870447"},{"key":"S0022481200017333_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935740"},{"key":"S0022481200017333_ref011","article-title":"Relevant implication and the case for a weaker logic","author":"Brady","journal-title":"Journal of Philosophical Logic"},{"key":"S0022481200017333_ref023","volume-title":"Relevant logics and their rivals","volume":"1","author":"Routley","year":"1982"},{"key":"S0022481200017333_ref005","volume-title":"A decision procedure for the system  of entailment with negation","author":"Belnap","year":"1961"},{"key":"S0022481200017333_ref024","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935747"},{"key":"S0022481200017333_ref013","unstructured":"Dunn J. M. , The algebra of intensional logics, Ph.D. Thesis , University of Pittsburgh, Pittsburgh, Pennsylvania, 1966."},{"key":"S0022481200017333_ref018","first-page":"235","article-title":"On the interpolation theorem of Craig","volume":"12","author":"Maehara","year":"1960","journal-title":"Sugaku"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017333","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T17:28:46Z","timestamp":1557682126000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017333\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S0022481200017333"],"URL":"https:\/\/doi.org\/10.2307\/2275666","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}