{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T18:04:26Z","timestamp":1785261866434,"version":"3.55.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":16186,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1969,11,17]]},"abstract":"<jats:p>By <jats:italic>\u03b3<\/jats:italic>, we mean the rule, \u201cFrom \u251c <jats:italic>A<\/jats:italic> and \u251c <jats:italic>\u0100<\/jats:italic> V <jats:italic>B<\/jats:italic>, infer \u251c <jats:italic>B<\/jats:italic>\u201d.<jats:sup>1<\/jats:sup> This rule has played an important and a controversial role in a set of <jats:italic>relevant logics<\/jats:italic> free of certain well-known paradoxes of implication, like <jats:italic>A\u0100-\u2192B<\/jats:italic> and <jats:italic>A-\u2192(B-\u2192B)<\/jats:italic>. Among these logics we count the pioneering systems of <jats:italic>strenge Implikation<\/jats:italic> presented by Ackermann in [1],<jats:sup>2<\/jats:sup> as well as the Anderson-Belnap systems E of entail-ment and R of relevant implication.<jats:sup>3<\/jats:sup><\/jats:p>","DOI":"10.2307\/2270909","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:55:37Z","timestamp":1146934537000},"page":"460-474","source":"Crossref","is-referenced-by-count":54,"title":["E, R AND <i>\u03b3<\/i>"],"prefix":"10.1017","volume":"34","author":[{"given":"Robert K.","family":"Meyer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Michael Dunn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200093750_ref018","first-page":"1","article-title":"Topological representation of distributive lattices and Brouwerian logics","volume":"67","author":"Stone","year":"1937","journal-title":"\u010casopis pro pe\u0161tov\u00e1n\u00ed matematiky a fysiky"},{"key":"S0022481200093750_ref017","volume-title":"Natural deduction. A proof-theoretical study","author":"Prawitz","year":"1965"},{"key":"S0022481200093750_ref016","doi-asserted-by":"publisher","DOI":"10.4288\/jafpos1956.2.183"},{"key":"S0022481200093750_ref004","first-page":"107","article-title":"Modalities in Ackermann's \u201crigorous implication\u201d","volume":"24","author":"Anderson","year":"1959","journal-title":"this Journal"},{"key":"S0022481200093750_ref007","first-page":"1","article-title":"Intensional models for first-degree formulas","volume":"32","author":"Belnap","year":"1967","journal-title":"this Journal"},{"key":"S0022481200093750_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF00818100"},{"key":"S0022481200093750_ref006","doi-asserted-by":"publisher","DOI":"10.1037\/e523212009-001"},{"key":"S0022481200093750_ref012","unstructured":"Meyer R. K. , R-mingle and relevant disjunction, Abstract, this Journal (to appear)."},{"key":"S0022481200093750_ref013","unstructured":"Meyer R. K. , Some problems no longer open for E and related logics, Abstract, this Journal (to appear)."},{"key":"S0022481200093750_ref001","first-page":"113","article-title":"Begr\u00fcndung einer strenge Implikation","volume":"21","author":"Ackermann","year":"1956","journal-title":"this Journal"},{"key":"S0022481200093750_ref002","first-page":"388","article-title":"Entailment shorn of modality","volume":"25","author":"Anderson","year":"1960","journal-title":"this Journal"},{"key":"S0022481200093750_ref009","unstructured":"Dunn J. M. , Algebraic completeness results for R-mingle and its extensions, this Journal (to appear)."},{"key":"S0022481200093750_ref003","first-page":"7","article-title":"Some open problems concerning the system E of entailment","volume":"16","author":"Anderson","year":"1963","journal-title":"Acta philosophica fennica"},{"key":"S0022481200093750_ref008","volume-title":"Foundations of mathematical logic","author":"Curry","year":"1963"},{"key":"S0022481200093750_ref011","unstructured":"Meyer R. K. , E and S4, Notre Dame journal of formal logic (to appear)."},{"key":"S0022481200093750_ref014","unstructured":"Meyer R. K. , A characteristic matrix for RM (unpublished)."},{"key":"S0022481200093750_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02052953"},{"key":"S0022481200093750_ref015","first-page":"1021","article-title":"Entailment logics and material implication, Abstract","volume":"15","author":"Meyer","year":"1968","journal-title":"Notices of the American Mathematical Society"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200093750","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T15:46:54Z","timestamp":1559404014000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200093750\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1969,11,17]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1969,11,17]]}},"alternative-id":["S0022481200093750"],"URL":"https:\/\/doi.org\/10.2307\/2270909","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1969,11,17]]}}}