{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:46Z","timestamp":1761611206111},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame\u2010theoretic. Roughly, given a normal logic <jats:italic>L<\/jats:italic> above K4.3, we enumerate effectively a class of (possibly infinite) frames with respect to which <jats:italic>L<\/jats:italic> is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a Harropstyle argument to establish the decidability of <jats:italic>L<\/jats:italic>, provided of course that it has finitely many axioms.<\/jats:p>","DOI":"10.1002\/malq.19950410103","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T23:51:17Z","timestamp":1180828277000},"page":"15-23","source":"Crossref","is-referenced-by-count":12,"title":["All Finitely Axiomatizable Normal Extensions of K4.3 are Decidable"],"prefix":"10.1002","volume":"41","author":[{"given":"Michael","family":"Zakharyaschevm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Alekseev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120129"},{"key":"e_1_2_1_3_2","first-page":"758","article-title":"A proof of Bull's theorem using the method of diagrams","volume":"58","author":"Corsi G.","year":"1993","journal-title":"J. Symbolic Logic"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19710170141"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272340"},{"key":"e_1_2_1_6_2","unstructured":"Goldblatt R. Logics of time and computation. CSLI Lecture Notes Number 7 (1987)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100033120"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19930390136"},{"key":"e_1_2_1_9_2","unstructured":"Maksimova L. Modal K4\u2010logics of the infinite slice. In: Proceedings of the IX. All\u2010Union Conference on Logic Methodology and Philosophy of Science Khar'kov 1986 p.35(in Russian)."},{"key":"e_1_2_1_10_2","first-page":"659","article-title":"Syntax and semantics of modal logics containing S4","volume":"27","author":"Zakharyaschev M.","year":"1988","journal-title":"Algebra i Logica"},{"key":"e_1_2_1_10_3","first-page":"408","volume":"27","year":"1988","journal-title":"English translation: Algebra and Logic"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275372"},{"key":"e_1_2_1_12_2","volume-title":"Canonical formulas for K4. Part II: Cofinal subframe logics. ILLC Prepublication Series, X\u201093\u201306","author":"Zakharyaschev M.","year":"1993"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:58:06Z","timestamp":1698256686000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410103"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410103","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}