{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:45:18Z","timestamp":1774953918413,"version":"3.50.1"},"reference-count":10,"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":5306,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In [60] N. Belnap presented an 8-element matrix for the relevant logic <jats:italic>R<\/jats:italic> with the following property: if in an implication <jats:italic>A<\/jats:italic> \u2192 <jats:italic>B<\/jats:italic> the formulas <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> do not have a common variable then there exists a valuation <jats:italic>v<\/jats:italic> such that <jats:italic>v<\/jats:italic> (<jats:italic>A<\/jats:italic> \u2192 <jats:italic>B<\/jats:italic>) does not belong to the set of designated elements of this matrix. A 6-element matrix of this kind can be found in: R. Routley, R.K. Meyer, V. Plumwood and R.T. Brady [82], Below we prove that the logics generated by these two matrices are the only maximal extensions of the relevant logic <jats:italic>R<\/jats:italic> which have the <jats:italic>relevance property<\/jats:italic>: if <jats:italic>A<\/jats:italic> \u2192 <jats:italic>B<\/jats:italic> is provable in such a logic then <jats:italic>A<\/jats:italic> and <jats:italic>B<\/jats:italic> have a common propositional variable.<\/jats:p>","DOI":"10.2307\/2586622","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T14:03:11Z","timestamp":1146924191000},"page":"1125-1154","source":"Crossref","is-referenced-by-count":10,"title":["There exist exactly two maximal strictly relevant extensions of the relevant logic <i>R<\/i>"],"prefix":"10.1017","volume":"64","author":[{"given":"Kazimierz","family":"Swirydowicz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200013232_ref004","first-page":"49","volume":"XLII","year":"1983","journal-title":"Stadia Logica"},{"key":"S0022481200013232_ref003","volume-title":"Algebraizable logics","year":"1989"},{"key":"S0022481200013232_ref002","first-page":"144","volume":"25","year":"1960","journal-title":"Entailment and relevance"},{"key":"S0022481200013232_ref011","volume-title":"Essays in the matrix semantics of relevant logics","year":"1980"},{"key":"S0022481200013232_ref005","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19900360606"},{"key":"S0022481200013232_ref010","volume-title":"Automated theorem proving in non-classical logics","year":"1988"},{"key":"S0022481200013232_ref008","first-page":"168","volume-title":"Truth, syntax and modality","year":"1973"},{"key":"S0022481200013232_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19700160703"},{"key":"S0022481200013232_ref006","first-page":"445","volume":"12","year":"1973","journal-title":"Algebra i Logika"},{"key":"S0022481200013232_ref009","volume-title":"Relevant logics and their rivals, Part 1","year":"1982"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200013232","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T16:38:16Z","timestamp":1557419896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200013232\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,9]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1999,9]]}},"alternative-id":["S0022481200013232"],"URL":"https:\/\/doi.org\/10.2307\/2586622","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,9]]}}}