{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T15:34:34Z","timestamp":1649086474875},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":16506,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1969,1]]},"abstract":"<jats:p>Kripke's model structure for D2 is a quadruple (<jats:italic>G, K, R, N<\/jats:italic>) where <jats:italic>N<\/jats:italic> is the set of normal elements, i.e., the subset of <jats:italic>K<\/jats:italic> such that for every <jats:italic>H<\/jats:italic> in <jats:italic>N, HRH.<\/jats:italic> (See [1, p. 220, p. 211].) In fact, however, this structure provides a model for E2, as the work of Lemmon shows ([2, pp. 58\u201362]).<\/jats:p><jats:p>To show the inadequacy of Kripke's model structure, we show that the E2 thesis \u25a1B \u2283 B, not a thesis of D2, is valid under Kripke's modelling for D2. Suppose, for a reductio argument, that \u25a1 B \u2283 B is false for some valuation \u03d5 in some D2 model structure. Theny\u03d5(\u25a1B \u2283 B, G) = F; so by truth-functional assignments<\/jats:p>","DOI":"10.2307\/2271364","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:50:27Z","timestamp":1146948627000},"page":"568-568","source":"Crossref","is-referenced-by-count":0,"title":["The inadequacy of Kripke's semantical analysis of D2 and D3"],"prefix":"10.1017","volume":"33","author":[{"given":"R.","family":"Routley","sequence":"first","affiliation":[]},{"given":"H.","family":"Montgomery","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120010917X_ref003","first-page":"191","article-title":"Algebraic semantics for modal logics. II","volume":"31","author":"Lemmon","year":"1966","journal-title":"this Journal"},{"key":"S002248120010917X_ref001","first-page":"206","volume-title":"Symposium on the theory of models","author":"Kripke","year":"1965"},{"key":"S002248120010917X_ref002","first-page":"46","article-title":"Algebraic semantics for modal logics. I","volume":"31","author":"Lemmon","year":"1966","journal-title":"this Journal"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120010917X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T20:39:57Z","timestamp":1559421597000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120010917X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1969,1]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1969,1]]}},"alternative-id":["S002248120010917X"],"URL":"https:\/\/doi.org\/10.2307\/2271364","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1969,1]]}}}