{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T13:26:29Z","timestamp":1708953989410},"reference-count":11,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4699,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1994,1]]},"abstract":"Abstract<\/jats:title>The logic CD<\/jats:bold> is an intermediate logic (stronger than intuitionistic logic and weaker than classical logic) which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD<\/jats:bold> has a Gentzen\u2010type formulation called LD<\/jats:bold> (which is same as LK<\/jats:bold> except that (\u2192) and (\u2283\u2013) rules are replaced by the corresponding intuitionistic rules) and that the cut\u2010elimination theorem does not hold for LD<\/jats:bold>. In this paper we present a modification of LD<\/jats:bold> and prove the cut\u2010elimination theorem for it. Moreover we prove a \u201cweak\u201d version of cut\u2010elimination theorem for LD<\/jats:bold>, saying that all \u201ccuts\u201d except some special forms can be eliminated from a proof in LD<\/jats:bold>. From these cut\u2010elimination theorems we obtain some corollaries on syntactical properties of CD<\/jats:bold>: fragments collapsing into intuitionistic logic. Harrop disjunction and existence properties, and a fact on the number of logical symbols in the axiom of CD<\/jats:bold>.<\/jats:p>Mathematics Subject Classification<\/jats:bold>: 03B55. 03F05.<\/jats:p>","DOI":"10.1002\/malq.19940400203","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:21:56Z","timestamp":1180200116000},"page":"153-172","source":"Crossref","is-referenced-by-count":9,"title":["Cut\u2010Elimination Theorem for the Logic of Constant Domains"],"prefix":"10.1002","volume":"40","author":[{"given":"Ryo","family":"Kashima","sequence":"first","affiliation":[]},{"given":"Tatsuya","family":"Shimura","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Intuitionistic Logic Model Theory and Forcing","author":"Fitting M. C.","year":"1969"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2977-2"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2270260"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(64)50066-9"},{"key":"e_1_2_1_6_2","unstructured":"Kashima R. Cut\u2010elimination theorem for the intermediate logic CD. Research Report on Information Sciences C\u2010100 (1991) Tokyo Institute of Technology."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273451"},{"key":"e_1_2_1_8_2","first-page":"53","article-title":"An intermediate predicate logic","volume":"14","author":"Nagashima T.","year":"1973","journal-title":"Hitotsubashi Journal of Arts and Sciences"},{"key":"e_1_2_1_9_2","first-page":"41","article-title":"Model extension theorem and Craig's interpolation theorem for intermediate predicate logics","volume":"15","author":"Ono H.","year":"1983","journal-title":"Reports Math. Logic"},{"key":"e_1_2_1_10_2","volume-title":"Proof Theory","author":"Takeuti G.","year":"1987"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2964756"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195524178"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19940400203","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19940400203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T02:45:12Z","timestamp":1698115512000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19940400203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["10.1002\/malq.19940400203"],"URL":"http:\/\/dx.doi.org\/10.1002\/malq.19940400203","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":["Logic"],"published":{"date-parts":[[1994,1]]}}}