{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T02:51:55Z","timestamp":1722480715923},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2018,9,27]],"date-time":"2018-09-27T00:00:00Z","timestamp":1538006400000},"content-version":"unspecified","delay-in-days":26,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2018,9]]},"abstract":"Abstract<\/jats:title>We add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionistic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical and intuitionistic logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for S4 and for H.<\/jats:p>","DOI":"10.1017\/s1755020318000229","type":"journal-article","created":{"date-parts":[[2018,9,27]],"date-time":"2018-09-27T09:59:57Z","timestamp":1538042397000},"page":"507-518","source":"Crossref","is-referenced-by-count":4,"title":["COMPLETENESS OF SECOND-ORDER PROPOSITIONAL S4 AND H IN TOPOLOGICAL SEMANTICS"],"prefix":"10.1017","volume":"11","author":[{"given":"PHILIP","family":"KREMER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,9,27]]},"reference":[{"key":"S1755020318000229_ref11","volume-title":"The Mathematics of Metamathematics","author":"Rasiowa","year":"1963"},{"key":"S1755020318000229_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/2275545"},{"key":"S1755020318000229_ref14","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1231082306"},{"key":"S1755020318000229_ref13","volume-title":"Lectures on the Curry-Howard Isomorphism","author":"S\u00f8rensen","year":"2006"},{"key":"S1755020318000229_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02015377"},{"key":"S1755020318000229_ref1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1970.tb00432.x"},{"key":"S1755020318000229_ref7","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1039724892"},{"key":"S1755020318000229_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020314000021"},{"key":"S1755020318000229_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020313000087"},{"key":"S1755020318000229_ref4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1305\/ndjfl\/1040067314","article-title":"The expressive power of second-order propositional modal logic","volume":"37","author":"Kaminski","year":"1996","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020318000229_ref10","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120131"},{"key":"S1755020318000229_ref5","first-page":"355","article-title":"S5 with quantifiable propositional variables","volume":"35","author":"Kaplan","year":"1970","journal-title":"Journal of Symbolic Logic"},{"key":"S1755020318000229_ref12","first-page":"69","article-title":"The intuitionistic propositional calculus with quantifiers (in Russian)","volume":"22","author":"Sobolev","year":"1977","journal-title":"Matematicheskiye Zametki"},{"key":"S1755020318000229_ref3","first-page":"131","volume-title":"Types for Proofs and Programs, International Workshop TYPES \u201993","volume":"Vol. 806","author":"Geuvers","year":"1994"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020318000229","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T21:19:12Z","timestamp":1555190352000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020318000229\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["S1755020318000229"],"URL":"https:\/\/doi.org\/10.1017\/s1755020318000229","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}