{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:17Z","timestamp":1761611177873},"reference-count":10,"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":10876,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,6]]},"abstract":"<jats:p>This work results from an attempt to give the vague notion of relevance a concrete semantical interpretation. The idea is that propositions may be divided into different \u201cdomains of relevance\u201d. Each \u201cdomain\u201d has its own \u201cT\u201d and \u201cF\u201d values, and propositions \u201cbelonging\u201d to one domain can never entail propositions \u201cbelonging\u201d to another, unconnected one.<\/jats:p><jats:p>The semantics we have developed were found to correspond to an already known system, which we call here <jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub>. Its axioms are the implication-negation axioms of the system <jats:bold>RM<\/jats:bold> ([1, Chapter 5]). However, as Meyer has shown, <jats:bold>RM<\/jats:bold> is not a conservative extension of <jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub>, since <jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub> has the sharing-of-variables property ([5], and [1, pp. 148\u2013149[), which the implication-negation fragment of <jats:bold>RM<\/jats:bold> has not.<\/jats:p><jats:p><jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub> has four advantages in comparison to its more famous sister <jats:bold>R<\/jats:bold><jats:sub>\u2972<\/jats:sub> (the pure intentional fragment of the system <jats:bold>R<\/jats:bold>; see [1]):<\/jats:p><jats:p>a) It has a very natural (from a relevance point of view) many-valued semantics, the simple form of which we describe here.<\/jats:p><jats:p>b) <jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub>, \u22a2 <jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub> \u2192 [<jats:italic>A<\/jats:italic><jats:sub>2<\/jats:sub> \u2192 (\u2026 \u2192 (<jats:italic>A<jats:sub>n<\/jats:sub><\/jats:italic> \u2192 <jats:italic>A<\/jats:italic>) \u2026)] iff there is a proof of <jats:italic>A<\/jats:italic> from the set {<jats:italic>A<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026, <jats:italic>A<jats:sub>n<\/jats:sub><\/jats:italic>} that actually uses all the members of this set. In <jats:bold>R<\/jats:bold><jats:sub>\u2972<\/jats:sub>, this holds only if we talk about \u201csequences\u201d instead of \u201csets\u201d. This is somewhat less intuitive (see [1, pp. 394\u2013395]).<\/jats:p><jats:p>c) <jats:bold>RMI<\/jats:bold><jats:sub>\u2972<\/jats:sub> is a maximal \u201cnatural\u201d relevance logic, in the sense that every proper extension of it limits the number of \u201cdomains of relevance\u201d (\u00a7III).<\/jats:p>","DOI":"10.2307\/2274169","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:08:28Z","timestamp":1146938908000},"page":"334-342","source":"Crossref","is-referenced-by-count":25,"title":["Relevant entailment\u2014semantics and formal systems"],"prefix":"10.1017","volume":"49","author":[{"given":"Arnon","family":"Avron","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200033429_ref009","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19560021003"},{"key":"S0022481200033429_ref002","volume-title":"The weak theory of implication","author":"Church","year":"1951"},{"key":"S0022481200033429_ref003","first-page":"1","article-title":"Algebraic completeness results for R-mingle and its extensions","volume":"35","author":"Dunn","year":"1970","journal-title":"this Journal"},{"key":"S0022481200033429_ref004","first-page":"366","volume":"36","author":"Meyer","year":"1977","journal-title":"R-mingle and relevant disjunction"},{"key":"S0022481200033429_ref008","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195520115"},{"key":"S0022481200033429_ref005","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093894720"},{"key":"S0022481200033429_ref010","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19720181903"},{"key":"S0022481200033429_ref006","volume-title":"Proof theory","author":"Takeuti","year":"1975"},{"key":"S0022481200033429_ref001","volume-title":"Entailment","volume":"1","author":"Anderson","year":"1975"},{"key":"S0022481200033429_ref007","first-page":"23","article-title":"Axiomatization of a partial system of three-valued calculus of propositions","volume":"1","author":"Soboci\u0144ski","year":"1952","journal-title":"The Journal of Computing Systems"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200033429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:48:29Z","timestamp":1558630109000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200033429\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1984,6]]}},"alternative-id":["S0022481200033429"],"URL":"https:\/\/doi.org\/10.2307\/2274169","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,6]]}}}