{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T01:40:04Z","timestamp":1721094004786},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T00:00:00Z","timestamp":1553212800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the article [2] a hierarchy of modal logics has been defined to capture the logical features of Bayesian belief revision. Elements in that hierarchy were distinguished by the cardinality of the set of elementary propositions. By linking the modal logics in the hierarchy to the modal logics of Medvedev frames it has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. However, the infinite case remained open. In this article we prove that the modal logic of Bayesian belief revision determined by standard Borel spaces (these cover probability spaces that occur in most of the applications) is also not finitely axiomatizable.<\/jats:p>","DOI":"10.1017\/s1755020319000157","type":"journal-article","created":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T07:27:50Z","timestamp":1553239670000},"page":"326-337","source":"Crossref","is-referenced-by-count":0,"title":["STANDARD BAYES LOGIC IS NOT FINITELY AXIOMATIZABLE"],"prefix":"10.1017","volume":"13","author":[{"given":"ZAL\u00c1N","family":"GYENIS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2019,3,22]]},"reference":[{"key":"S1755020319000157_ref11","first-page":"798","article-title":"The logic of infinite problems and the Kripke models on atomic semilattices of sets","volume":"245","author":"Skvortsov","year":"1979","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S1755020319000157_ref12","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199228003.001.0001"},{"key":"S1755020319000157_ref7","first-page":"83","article-title":"Characterization of Medvedev\u2019s logic by means of Kubi\u0144ski\u2019s frames","volume":"42","author":"\u0141azarz","year":"2013","journal-title":"Bulletin of the Section of Logic"},{"key":"S1755020319000157_ref2","article-title":"The modal logic of Bayesian belief revision","author":"Brown","year":"2018","journal-title":"Journal of Philosophical Logic"},{"key":"S1755020319000157_ref9","first-page":"103","article-title":"Structural completeness of Medvedev\u2019s propositional calculus","volume":"6","author":"Prucnal","year":"1976","journal-title":"Reports on Mathematical Logic"},{"key":"S1755020319000157_ref3","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal Logic","author":"Chagrov","year":"1997"},{"key":"S1755020319000157_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370370"},{"key":"S1755020319000157_ref1","volume-title":"Modal Logic","author":"Blackburn","year":"2002"},{"key":"S1755020319000157_ref4","volume-title":"Some alternatives to Bayes\u2019 rule","author":"Diaconis","year":"1983"},{"key":"S1755020319000157_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-016-9680-1"},{"key":"S1755020319000157_ref8","first-page":"20","article-title":"On the interpretation of the logical formulas by means of finite problems","volume":"169","author":"Medvedev","year":"1996","journal-title":"Doklady Akademii Nauk SSSR"},{"key":"S1755020319000157_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020319000157","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T01:18:08Z","timestamp":1721092688000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020319000157\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,22]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["S1755020319000157"],"URL":"https:\/\/doi.org\/10.1017\/s1755020319000157","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,22]]}}}