{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T17:39:22Z","timestamp":1784914762270,"version":"3.55.0"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3298,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Several extensions of the basic modal language are characterized in terms of interpolation. Our main results are of the following form: <jats:italic>Language L\u2032 is the least expressive extension of L with interpolation<\/jats:italic>. For instance, let \u2133(D) be the extension of the basic modal language with a difference operator [7], First-order logic is the least expressive extension of \u2133(D) with interpolation. These characterizations are subsequently used to derive new results about hybrid logic, relation algebra and the guarded fragment.<\/jats:p>","DOI":"10.2178\/jsl\/1107298517","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T16:57:08Z","timestamp":1109782628000},"page":"223-234","source":"Crossref","is-referenced-by-count":41,"title":["Interpolation for extended modal languages"],"prefix":"10.1017","volume":"70","author":[{"given":"Balder","family":"ten Cate","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000726X_ref007","first-page":"566","volume":"57","author":"de Rijke","year":"1992","journal-title":"The modal logic of inequality"},{"key":"S002248120000726X_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059541"},{"key":"S002248120000726X_ref014","volume-title":"Liber Amicorum Dick de Jongh","author":"ten Cate","year":"2004"},{"key":"S002248120000726X_ref002","first-page":"977","volume":"66","author":"Areces","year":"2001","journal-title":"Hybrid logics: Characterization, interpolation and complexity"},{"key":"S002248120000726X_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S002248120000726X_ref013","unstructured":"Spaan Edith , Complexity of modal logics, Ph.D. thesis , ILLC, University of Amsterdam, 1993."},{"key":"S002248120000726X_ref001","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004275029985"},{"key":"S002248120000726X_ref006","first-page":"250","volume":"22","author":"Craig","year":"1957","journal-title":"Linear reasoning, a new form of the Herbrand-Gentzen theorem"},{"key":"S002248120000726X_ref015","first-page":"695","volume-title":"Algebraic logic","author":"Venema","year":"1991"},{"key":"S002248120000726X_ref005","unstructured":"Conradie Willem , Definability and changing perspectives: The Beth property for three extensions of modal logic, Master's thesis , ILLC, University of Amsterdam, 2002."},{"key":"S002248120000726X_ref003","volume-title":"Model-theoretic logics","author":"Barwise","year":"1985"},{"key":"S002248120000726X_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01054038"},{"key":"S002248120000726X_ref010","first-page":"1719","volume":"64","author":"Gr\u00e4del","year":"1999","journal-title":"On the restraining power of guards"},{"key":"S002248120000726X_ref012","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/11.5.691"},{"key":"S002248120000726X_ref011","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015154431342"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000726X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T17:15:40Z","timestamp":1556903740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000726X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2005,3]]}},"alternative-id":["S002248120000726X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1107298517","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}