{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,24]],"date-time":"2025-05-24T04:09:29Z","timestamp":1748059769131},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,11,6]],"date-time":"2014-11-06T00:00:00Z","timestamp":1415232000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Spectrum Exchangeability, Sx, is an irrelevance principle of Pure Inductive Logic, and arguably the most natural (but not the only) extension of Atom Exchangeability to polyadic languages. It has been shown<jats:sup>1<\/jats:sup>that all probability functions which satisfy Sx are comprised of a mixture of two essential types of probability functions; heterogeneous and homogeneous functions. We determine the theory of Spectrum Exchangeability, which for a fixed language<jats:italic>L<\/jats:italic>is the set of sentences of<jats:italic>L<\/jats:italic>which must be assigned probability 1 by every probability function satisfying Sx, by examining separately the theories of heterogeneity and homogeneity. We find that the theory of Sx is equal to the theory of finite structures, i.e., those sentences true in all finite structures for<jats:italic>L<\/jats:italic>, and it emerges that Sx is inconsistent with the principle of Super-Regularity (Universal Certainty). As a further consequence we are able to characterize those probability functions which satisfy Sx and the Finite Values Property.<\/jats:p>","DOI":"10.1017\/s1755020314000331","type":"journal-article","created":{"date-parts":[[2014,11,6]],"date-time":"2014-11-06T09:48:24Z","timestamp":1415267304000},"page":"108-130","source":"Crossref","is-referenced-by-count":1,"title":["THE THEORY OF SPECTRUM EXCHANGEABILITY"],"prefix":"10.1017","volume":"8","author":[{"given":"E.","family":"HOWARTH","sequence":"first","affiliation":[]},{"given":"J. B.","family":"PARIS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,11,6]]},"reference":[{"key":"S1755020314000331_ref16","first-page":"569","article-title":"The impossibility of an algorithm for the decidability problem on finite classes","volume":"70","author":"Trakhtenbrot","year":"1950","journal-title":"Proceedings of the USSR Academy of Sciences"},{"key":"S1755020314000331_ref6","unstructured":"Landes J . (2009). The principle of spectrum exchangeability within inductive logic. PhD Thesis, University of Manchester. Available from: http:\/\/www.maths.manchester.ac.uk\/\u223cjeff\/."},{"key":"S1755020314000331_ref15","unstructured":"Paris J. B. , & Vencovsk\u00e1 A . (To appear). Pure Inductive Logic. Perspectives in Mathematical Logic, The Association of Symbolic Logic Series. Cambridge: Cambridge University Press."},{"key":"S1755020314000331_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2009.07.001"},{"key":"S1755020314000331_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759729"},{"key":"S1755020314000331_ref11","volume-title":"The Uncertain Reasoner\u2019s Companion","author":"Paris","year":"1994"},{"key":"S1755020314000331_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0714-6_12"},{"key":"S1755020314000331_ref2","volume-title":"Theory of Probability, Volume 1","author":"de Finetti","year":"1974"},{"key":"S1755020314000331_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-007-9066-y"},{"key":"S1755020314000331_ref12","first-page":"428","volume-title":"The Continuum Companion to Philosophical Logic","author":"Paris","year":"2011"},{"key":"S1755020314000331_ref1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1525\/9780520318328-002","volume-title":"Studies in Inductive Logic and Probability, Volume II","author":"Carnap","year":"1980"},{"key":"S1755020314000331_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-008-9140-7"},{"key":"S1755020314000331_ref9","unstructured":"Nix C. J . (2005). Probabilistic induction in the predicate calculus. PhD Thesis, University of Manchester, UK. Available from: http:\/\/www.maths.manchester.ac.uk\/\u223cjeff\/."},{"key":"S1755020314000331_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200051756"},{"key":"S1755020314000331_ref5","unstructured":"Howarth E . (Forthcoming). New rationality principles in pure inductive logic. PhD Thesis, University of Manchester. To appear at http:\/\/www.maths.manchester.ac.uk\/\u223cjeff\/."},{"key":"S1755020314000331_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13962-8_38"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020314000331","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T12:14:54Z","timestamp":1650543294000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020314000331\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,6]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["S1755020314000331"],"URL":"https:\/\/doi.org\/10.1017\/s1755020314000331","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,6]]}}}