{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:19Z","timestamp":1761611179783},"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":"<jats:title>Abstract<\/jats:title><jats:p>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 <jats:bold>S4<\/jats:bold>, first with propositional quantifiers, to the system <jats:bold>S4<jats:italic>\u03c0<\/jats:italic><\/jats:bold>+; and then with definite propositional descriptions, to the system <jats:bold>S4<jats:italic>\u03c0<\/jats:italic><\/jats:bold>+<jats:sup><jats:italic>ip<\/jats:italic><\/jats:sup>. We show that relevant implication can in some sense be defined in the modal system <jats:bold>S4<jats:italic>\u03c0<\/jats:italic><\/jats:bold>+<jats:sup><jats:italic>ip<\/jats:italic><\/jats:sup>, although it cannot be defined in <jats:bold>S4<jats:italic>\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 <b>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]]}}}