{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T20:46:05Z","timestamp":1783111565560,"version":"3.54.6"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T00:00:00Z","timestamp":1722211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["18ZDA033"],"award-info":[{"award-number":["18ZDA033"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s11225-024-10145-x","type":"journal-article","created":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T04:02:16Z","timestamp":1722225736000},"page":"1543-1566","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The McKinsey Axiom on Weakly Transitive Frames"],"prefix":"10.1007","volume":"113","author":[{"given":"Qian","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minghui","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,29]]},"reference":[{"key":"10145_CR1","doi-asserted-by":"publisher","first-page":"55","DOI":"10.2307\/2272270","volume":"40","author":"J van Benthem","year":"1975","unstructured":"van Benthem, J., A note on modal formulas and relational properties, The Journal of Symbolic Logic 40: 55\u201358, 1975.","journal-title":"The Journal of Symbolic Logic"},{"key":"10145_CR2","doi-asserted-by":"publisher","first-page":"301","DOI":"10.2307\/2272228","volume":"41","author":"J van Benthem","year":"1976","unstructured":"van Benthem, J., Modal reduction principles, The Journal of Symbolic Logic 41: 301\u2013312, 1976.","journal-title":"The Journal of Symbolic Logic"},{"key":"10145_CR3","unstructured":"van Benthem,\u00a0J., Modal Correspondence Theory, Ph.D. thesis, University of Amsterdam, 1976."},{"key":"10145_CR4","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s11225-011-9348-9","volume":"99","author":"G Bezhanishvili","year":"2011","unstructured":"Bezhanishvili, G., and N. Bezhanishvili, An algebraic approach to canonical formulas: modal case, Studia Logica 99: 93\u2013125, 2011.","journal-title":"Studia Logica"},{"issue":"3","key":"10145_CR5","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s11225-005-4648-6","volume":"81","author":"G Bezhanishvili","year":"2005","unstructured":"Bezhanishvili, G., L. Esakia, and D. Gabelaia, Some results on modal axiomatization and definability for topological spaces, Studia Logica 81(3): 325\u2013355, 2005.","journal-title":"Studia Logica"},{"key":"10145_CR6","doi-asserted-by":"crossref","unstructured":"Bezhanishvili, G., L. Esakia, and D. Gabelaia, Spectral and $$T_0$$-spaces in d-semantics, in N. Bezhanishvili, S. L\u00f6bner, K. Schwabe, and L. Spada, (eds.), Logic, Language, and Computation, TbiLLC 2009, LNCS 6618, Springer, 2009, pp. 16\u201329.","DOI":"10.1007\/978-3-642-22303-7_2"},{"issue":"1","key":"10145_CR7","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1017\/S1755020309990335","volume":"3","author":"G Bezhanishvili","year":"2010","unstructured":"Bezhanishvili, G., L. Esakia, and D. Gabelaia, The modal logic of stone spaces: diamond as derivative, The Review of Symbolic Logic 3(1): 26\u201340, 2010.","journal-title":"The Review of Symbolic Logic"},{"key":"10145_CR8","doi-asserted-by":"crossref","unstructured":"Bezhanishvili, G., S. Ghilardi, and M. Jibladze, An algebraic approach to subframe logics. modal case, Notre Dame Journal of Formal Logic 52(2): 187\u2013202, 2011.","DOI":"10.1215\/00294527-1306190"},{"key":"10145_CR9","doi-asserted-by":"crossref","unstructured":"Blackburn,\u00a0P., M.\u00a0de\u00a0Rijke, and Y.\u00a0Venema, Modal Logic, Cambridge University Press, 2001.","DOI":"10.1017\/CBO9781107050884"},{"key":"10145_CR10","volume-title":"Modal Logic","author":"A Chagrov","year":"2001","unstructured":"Chagrov,\u00a0A., and M.\u00a0Zakharyaschev, Modal Logic, Oxford, Clarendon Press, 2001."},{"key":"10145_CR11","unstructured":"Church,\u00a0A., Introduction to Mathematical Logic, Princeton University Press, 1956."},{"key":"10145_CR12","volume-title":"Weak transitivity-a restitution, Logical Investigations 8: 244\u2013255","author":"L Esakia","year":"2001","unstructured":"Esakia, L., Weak transitivity-a restitution, Logical Investigations 8: 244\u2013255, Nauka, Moscow, 2001 (in Russian)."},{"issue":"1\u20133","key":"10145_CR13","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.apal.2003.11.013","volume":"127","author":"L Esakia","year":"2004","unstructured":"Esakia, L., Intuitionistic logic and modality via topology, Annals of Pure and Applied Logic 127(1\u20133): 155\u2013170, 2004.","journal-title":"Annals of Pure and Applied Logic"},{"key":"10145_CR14","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1305\/ndjfl\/1093891703","volume":"16","author":"K Fine","year":"1975","unstructured":"Fine, K., Normal forms in modal logic, Notre Dame Journal of Formal Logic 16: 229\u2013237, 1975.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"10145_CR15","doi-asserted-by":"publisher","first-page":"35","DOI":"10.2307\/2272267","volume":"40","author":"R Goldblatt","year":"1975","unstructured":"Goldblatt, R., First-order definability in modal logic, The Journal of Symbolic Logic 40: 35\u201340, 1975.","journal-title":"The Journal of Symbolic Logic"},{"issue":"2","key":"10145_CR16","doi-asserted-by":"publisher","first-page":"554","DOI":"10.2307\/2274699","volume":"56","author":"R Goldblatt","year":"1991","unstructured":"Goldblatt, R., The McKinsey axiom is not canonical, The Journal of Symbolic Logic 56(2): 554\u2013562, 1991.","journal-title":"The Journal of Symbolic Logic"},{"key":"10145_CR17","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S1570-8683(03)00008-9","volume":"1","author":"R Goldblatt","year":"2003","unstructured":"Goldblatt, R., Mathematical modal logic: A view of its evolution, Journal of Applied Logic 1: 309\u2013392, 2003.","journal-title":"Journal of Applied Logic"},{"key":"10145_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.26686\/ajl.v5i0.1783","volume":"5","author":"R Goldblatt","year":"2007","unstructured":"Goldblatt, R., and I. Hodkinson, The McKinsey-Lemmon logic is barely canonical, Australasian Journal of Logic 5: 1\u201319, 2007.","journal-title":"Australasian Journal of Logic"},{"key":"10145_CR19","volume-title":"An Introduction to Modal Logic","author":"EJ Lemmon","year":"1977","unstructured":"Lemmon,\u00a0E.\u00a0J., An Introduction to Modal Logic, Basil Blackwell, Oxford, 1977."},{"key":"10145_CR20","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s11225-022-10027-0","volume":"111","author":"M Ma","year":"2023","unstructured":"Ma, M., and Q. Chen, Finite model property in weakly transitive tense logics, Studia Logica 111: 217\u2013250, 2023.","journal-title":"Studia Logica"},{"key":"10145_CR21","doi-asserted-by":"publisher","first-page":"141","DOI":"10.2307\/1969080","volume":"45","author":"JCC McKinsey","year":"1944","unstructured":"McKinsey, J. C. C., and A. Tarski, Algebra of topology, Annals of Mathematics 45: 141\u2013191, 1944.","journal-title":"Annals of Mathematics"},{"key":"10145_CR22","doi-asserted-by":"publisher","first-page":"83","DOI":"10.2307\/2267027","volume":"10","author":"JCC McKinsey","year":"1945","unstructured":"McKinsey, J. C. C., On the syntactical construction of systems of modal logic, The Journal of Symbolic Logic 10: 83\u201394, 1945.","journal-title":"The Journal of Symbolic Logic"},{"key":"10145_CR23","doi-asserted-by":"crossref","unstructured":"Sahlqvist, H., Completeness and correspondence in the first and second order semantics for modal logic, in S. Kanger, (ed.), Proceedings of the Third Scandinavian Logic Symposium, North-Holland Publishing Company, 1975, pp. 110\u2013143.","DOI":"10.1016\/S0049-237X(08)70728-6"},{"key":"10145_CR24","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1305\/ndjfl\/1093957741","volume":"5","author":"B Soboci\u0144ski","year":"1964","unstructured":"Soboci\u0144ski, B., Remarks about axiomatizations of certain modal systems, Notre Dame Journal of Formal Logic 5: 71\u201380, 1964.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"10145_CR25","doi-asserted-by":"crossref","unstructured":"Zakharyaschev, M., Canonical formulas for K4. part III: the finite model property, The Journal of Symbolic Logic 62(3): 950 \u2013 975, 1997.","DOI":"10.2307\/2275581"}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-024-10145-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11225-024-10145-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-024-10145-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T13:01:25Z","timestamp":1762434085000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11225-024-10145-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,29]]},"references-count":25,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10145"],"URL":"https:\/\/doi.org\/10.1007\/s11225-024-10145-x","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"value":"0039-3215","type":"print"},{"value":"1572-8730","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,29]]},"assertion":[{"value":"12 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}