{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T10:02:24Z","timestamp":1713952944231},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5945,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1997,12]]},"abstract":"Abstract<\/jats:title>R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was \u2018no\u2019. In the present paper, we extend S4<\/jats:bold>, first with propositional quantifiers, to the system S4\u03c0<\/jats:italic><\/jats:bold>+; and then with definite propositional descriptions, to the system S4\u03c0<\/jats:italic><\/jats:bold>+ip<\/jats:italic><\/jats:sup>. We show that relevant implication can in some sense be defined in the modal system S4\u03c0<\/jats:italic><\/jats:bold>+ip<\/jats:italic><\/jats:sup>, although it cannot be defined in S4\u03c0<\/jats:italic><\/jats:bold>+.<\/jats:p>","DOI":"10.2307\/2275626","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T23:03:06Z","timestamp":1146956586000},"page":"1057-1069","source":"Crossref","is-referenced-by-count":3,"title":["Defining relevant implication in a propositionally quantified S4<\/b>"],"prefix":"10.1017","volume":"62","author":[{"given":"Philip","family":"Kremer","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200015589_ref012","unstructured":"Kremer P. , On the complexity of propositional quantification in intuitionistic logic, forthcoming in this Journal."},{"key":"S0022481200015589_ref020","volume-title":"Introduction to mathematical philosophy","author":"Russell","year":"1919"},{"key":"S0022481200015589_ref003","volume-title":"Meaning and necessity","author":"Carnap","year":"1947"},{"key":"S0022481200015589_ref013","unstructured":"Kremer P. , Prepositional quantification in the topological semantics for S4 , manuscript."},{"key":"S0022481200015589_ref017","first-page":"462","volume-title":"Relevance is not reducible to modality","author":"Meyer","year":"1975"},{"key":"S0022481200015589_ref016","volume-title":"Symbolic logic","author":"Lewis","year":"1932"},{"key":"S0022481200015589_ref021","first-page":"159","volume":"37","author":"Urquhart","year":"1972","journal-title":"Semantics for relevant logics"},{"key":"S0022481200015589_ref002","first-page":"257","volume":"34","author":"Bull","year":"1969","journal-title":"On modal logic with prepositional quantifiers"},{"key":"S0022481200015589_ref018","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71541-6"},{"key":"S0022481200015589_ref014","first-page":"334","volume":"58","author":"Kremer","year":"1993","journal-title":"Quantifying ever propositions in relevance logic: non-axiomatisability of \u2200p and \u2203p"},{"key":"S0022481200015589_ref008","volume-title":"An introduction to modal logic","author":"Hughes","year":"1968"},{"key":"S0022481200015589_ref019","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/XIV.4.479"},{"key":"S0022481200015589_ref007","volume-title":"Grundlagen der Mathematik I","author":"Hilbert","year":"1934"},{"key":"S0022481200015589_ref009","volume-title":"A companion to modal logic","author":"Hughes","year":"1984"},{"key":"S0022481200015589_ref010","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1305\/ndjfl\/1040067314","article-title":"The expressive power of second-order prepositional modal logic","volume":"37","author":"Kaminski","year":"1996","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200015589_ref001","volume-title":"Entailment: the logic of relevance and necessity","volume":"1","author":"Anderson","year":"1975"},{"key":"S0022481200015589_ref005","first-page":"25","article-title":"\u00dcber sinn und bedeutung","volume":"100","author":"Frege","year":"1892","journal-title":"Zeitschrift f\u00fcr Philosophie und Kritik"},{"key":"S0022481200015589_ref015","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19630090502"},{"key":"S0022481200015589_ref006","first-page":"81","volume":"15","author":"Henkin","year":"1950","journal-title":"Completeness in the theory of types"},{"key":"S0022481200015589_ref011","first-page":"355","volume":"35","author":"Kaplan","year":"1970","journal-title":"S5 with quantifiablepropositional variables"},{"key":"S0022481200015589_ref004","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1970.tb00432.x"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200015589","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T19:55:36Z","timestamp":1557604536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200015589\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,12]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,12]]}},"alternative-id":["S0022481200015589"],"URL":"https:\/\/doi.org\/10.2307\/2275626","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,12]]}}}