{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:29:25Z","timestamp":1675211365056},"reference-count":17,"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>We establish cut-free left-handed Gentzenizations for a range of major relevant logics from B through to R, all with distribution. B is the basic system of the Routley-Meyer semantics (see [15], pp. 287\u2013300) and R is the logic of relevant implication (see [1], p. 341). Previously, the contractionless logics DW, TW, EW, RW and RWK were Gentzenized in [3], [4] and [5], and also the distributionless logics LBQ, LDWQ, LTWQ<jats:sup>o<\/jats:sup>, LEWQ<jats:sup>ot<\/jats:sup>, LRWQ, LRWKQ and LRQ in [6] and [7]. This paper provides Gentzenizations for the logics DJ, TJ, T and R, with various levels of contraction, and for the contractionless logic B, which could not be included in [4] using the technique developed there. We also include the Gentzenization of TW in order to compare it with that in [4]. The Gentzenizations that we obtain here for DW and RW are inferior to those already obtained in [4], but they are included for reference when constructing other systems. The logics EW and E present a difficulty for our method and are omitted. For background to the Gentzenization of relevant logics, see [6], and for motivation behind the logics involved, see [6], [1] and [15]. Because of the number of properties that are brought to bear in obtaining these systems, we prefer to consider Gentzenizations for particular logics rather than for arbitrary bunches of axioms.<\/jats:p>","DOI":"10.2307\/2275668","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:58:29Z","timestamp":1146956309000},"page":"402-420","source":"Crossref","is-referenced-by-count":7,"title":["Gentzenizations of relevant logics with distribution"],"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":"S0022481200017357_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01349561"},{"key":"S0022481200017357_ref007","unstructured":"Brady R. T. , Gentzenizations of relevant logics without distribution. II, this Journal, later."},{"key":"S0022481200017357_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF00211185"},{"key":"S0022481200017357_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/BF00248640"},{"key":"S0022481200017357_ref005","volume-title":"Logique et Analyse","author":"Brady"},{"key":"S0022481200017357_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370629"},{"key":"S0022481200017357_ref012","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF02120493","article-title":"Classical relevant logics. II","volume":"33","author":"Brady","year":"1974","journal-title":"Studia Logica"},{"key":"S0022481200017357_ref015","volume-title":"Relevant logics and their rivals","volume":"1","author":"Routley","year":"1982"},{"key":"S0022481200017357_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF00284976"},{"key":"S0022481200017357_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF00454743"},{"key":"S0022481200017357_ref017","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093637560"},{"key":"S0022481200017357_ref001","volume-title":"Entailment: The Logic of Relevance and Necessity","volume":"1","author":"Anderson","year":"1975"},{"key":"S0022481200017357_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249674"},{"key":"S0022481200017357_ref006","unstructured":"Brady R. T. , Gentzenizations of relevant logics without distribution. I, this Journal, later."},{"key":"S0022481200017357_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02123812"},{"key":"S0022481200017357_ref010","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093887722"},{"key":"S0022481200017357_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935747"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017357","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T21:28:30Z","timestamp":1557696510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017357\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,6]]}},"alternative-id":["S0022481200017357"],"URL":"https:\/\/doi.org\/10.2307\/2275668","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6]]}}}