{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T22:23:35Z","timestamp":1791411815232,"version":"4.3.3"},"reference-count":14,"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":7132,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a sequent calculus for the modal logic <jats:bold>S4<\/jats:bold>, and building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings into axioms and modal rules) we show how <jats:bold>S4<\/jats:bold> can easily be translated into full prepositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities (exponentials) only in correspondence with <jats:bold>S4<\/jats:bold> modalities. We discuss the complexity of the decision problem for several classes of linear formulas naturally arising from the proposed translations.<\/jats:p>","DOI":"10.2307\/2275915","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:52:43Z","timestamp":1146955963000},"page":"888-899","source":"Crossref","is-referenced-by-count":8,"title":["A modal view of linear logic"],"prefix":"10.1017","volume":"59","author":[{"given":"Simone","family":"Martini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Masini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200019587_ref006","volume-title":"Acta Universitatis Stockolmiensis, Stockolm Studies in Philosophy","volume":"1","author":"Kanger","year":"1957"},{"key":"S0022481200019587_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(92)90075-B"},{"key":"S0022481200019587_ref005","first-page":"135\u2013171","volume-title":"Issledovanija po formalizovannym jazykam i n\u00e9klassiceskim logikam","author":"Grishin","year":"1974"},{"key":"S0022481200019587_ref012","first-page":"215\u2013229","volume-title":"Contributions to mathematical logic, Logic Colloquium 1966","author":"Prawitz","year":"1968"},{"key":"S0022481200019587_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"S0022481200019587_ref002","volume-title":"Modal logics","author":"Dopp","year":"1965"},{"key":"S0022481200019587_ref014","volume-title":"Modal logic, the Lewis modal systems","author":"Zeman","year":"1973"},{"key":"S0022481200019587_ref003","volume-title":"Computers and intractability","author":"Garey","year":"1979"},{"key":"S0022481200019587_ref007","volume-title":"Series A I. Mathematica Dissertationes","volume":"23","author":"Ketonen","year":"1944"},{"key":"S0022481200019587_ref001","volume-title":"Foundations of mathematical logic","author":"Curry","year":"1977"},{"key":"S0022481200019587_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90041-B"},{"key":"S0022481200019587_ref010","first-page":"113\u2013130","article-title":"Gentzen method in modal calculi I","volume":"9","author":"Ohnishi","year":"1957","journal-title":"Osaka Mathematical Journal"},{"key":"S0022481200019587_ref011","first-page":"95\u2013104","volume-title":"Mathematical Logic","author":"Ono","year":"1990"},{"key":"S0022481200019587_ref013","volume-title":"CSLI Lecture Notes","volume":"29","author":"Troelstra","year":"1991"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200019587","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T03:16:08Z","timestamp":1557890168000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200019587\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1994,9]]}},"alternative-id":["S0022481200019587"],"URL":"https:\/\/doi.org\/10.2307\/2275915","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}