{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T04:07:14Z","timestamp":1750478834552,"version":"3.41.0"},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T00:00:00Z","timestamp":1254700800000},"content-version":"unspecified","delay-in-days":34,"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":[[2009,9]]},"abstract":"<jats:p>Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth\u2019s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, <jats:italic>reducibility<\/jats:italic>, is introduced; it is shown that in multimodal logics, explicit definability is equivalent to the combination of implicit definability and reducibility. The three notions of definability are characterized semantically using <jats:italic>(modal) algebras<\/jats:italic>. The use of algebras, rather than frames, is shown to be necessary for these characterizations.<\/jats:p>","DOI":"10.1017\/s175502030999013x","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T16:58:53Z","timestamp":1254761933000},"page":"451-468","source":"Crossref","is-referenced-by-count":4,"title":["ON DEFINABILITY IN MULTIMODAL LOGIC"],"prefix":"10.1017","volume":"2","author":[{"given":"JOSEPH Y.","family":"HALPERN","sequence":"first","affiliation":[]},{"given":"DOV","family":"SAMET","sequence":"additional","affiliation":[]},{"given":"ELLA","family":"SEGEV","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,10,5]]},"reference":[{"key":"S175502030999013X_manual_ref-9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00205012"},{"key":"S175502030999013X_manual_ref-5","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/3.2.173"},{"key":"S175502030999013X_manual_ref-8","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(99)80001-9"},{"key":"S175502030999013X_manual_ref-4","article-title":"Defining knowledge in terms of belief: the modal logic perspective","author":"Halpern","year":"2008","journal-title":"Review of Symbolic Logic"},{"key":"S175502030999013X_manual_ref-2","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(53)50042-3"},{"key":"S175502030999013X_manual_ref-3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S175502030999013X_manual_ref-1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004275029985"},{"key":"S175502030999013X_manual_ref-6","doi-asserted-by":"publisher","DOI":"10.2307\/2372123"},{"key":"S175502030999013X_manual_ref-7","doi-asserted-by":"publisher","DOI":"10.2307\/2372074"},{"key":"S175502030999013X_manual_ref-10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00971028"},{"key":"S175502030999013X_manual_ref-11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02259848"},{"key":"S175502030999013X_manual_ref-12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024248828122"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S175502030999013X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T22:26:27Z","timestamp":1750458387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S175502030999013X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S175502030999013X"],"URL":"https:\/\/doi.org\/10.1017\/s175502030999013x","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"type":"print","value":"1755-0203"},{"type":"electronic","value":"1755-0211"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}