{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T21:27:47Z","timestamp":1713562067268},"reference-count":20,"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":4394,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,3]]},"abstract":"Abstract<\/jats:title>We prove that everyn<\/jats:italic>-modal logic betweenK<\/jats:bold>n<\/jats:italic><\/jats:sup>andS5<\/jats:bold>n<\/jats:italic><\/jats:sup>is undecidable, whenever n \u2265 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov\u2013Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the (undecidable) representation problem of finite relation algebras.<\/jats:p>","DOI":"10.2178\/jsl\/1190150040","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:12:10Z","timestamp":1197573130000},"page":"221-234","source":"Crossref","is-referenced-by-count":30,"title":["On modal logics betweenK \u00d7 K \u00d7 K<\/b>andS5 \u00d7 S5 \u00d7 S5<\/b>"],"prefix":"10.1017","volume":"67","author":[{"given":"R.","family":"Hirsch","sequence":"first","affiliation":[]},{"given":"I.","family":"Hodkinson","sequence":"additional","affiliation":[]},{"given":"A.","family":"Kurucz","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009956_ref015","unstructured":"Monk J. 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