{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T07:48:51Z","timestamp":1773820131854,"version":"3.50.1"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T00:00:00Z","timestamp":1467158400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>In this article we describe a bunch of<jats:italic>probability logics with quantifiers over events<\/jats:italic>, and develop primary techniques for proving computational complexity results (in terms of<jats:italic>m<\/jats:italic>-degrees) about these logics, mainly over discrete probability spaces. Also the article contains a comparison with some other probability logics and a discussion of interesting analogies with research in the metamathematics of Boolean algebras, demonstrating a number of attractive features and intuitive advantages of the present proposal.<\/jats:p>","DOI":"10.1017\/s0960129516000189","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T06:47:32Z","timestamp":1467182852000},"page":"1581-1600","source":"Crossref","is-referenced-by-count":8,"title":["Quantifying over events in probability logic: an introduction"],"prefix":"10.1017","volume":"27","author":[{"given":"STANISLAV O.","family":"SPERANSKI","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,6,29]]},"reference":[{"key":"S0960129516000189_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01459101"},{"key":"S0960129516000189_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"},{"key":"S0960129516000189_ref3","volume-title":"Probability and Measure","author":"Billingsley","year":"1995"},{"key":"S0960129516000189_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0328-9"},{"key":"S0960129516000189_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2013.06.015"},{"key":"S0960129516000189_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59207-2"},{"key":"S0960129516000189_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190967"},{"key":"S0960129516000189_ref8","first-page":"1","volume-title":"Handbook of Boolean Algebras","author":"Koppelberg","year":"1989"},{"key":"S0960129516000189_ref13","volume-title":"Theory of Recursive Functions and Effective Computability","author":"Rogers","year":"1967"},{"key":"S0960129516000189_ref20","first-page":"267","volume-title":"Conference Proceedings Vol. 60, Waves, Information and Foundations of Physics","author":"Suppes","year":"1998"},{"key":"S0960129516000189_ref7","first-page":"509","volume-title":"Model-Theoretic Logics","author":"Keisler","year":"1985"},{"key":"S0960129516000189_ref17","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exs041"},{"key":"S0960129516000189_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(90)90060-U"},{"key":"S0960129516000189_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-011-9148-3"},{"key":"S0960129516000189_ref10","volume-title":"The Oxford Handbook of Probability and Philosophy","author":"Leitgeb","year":"2016"},{"key":"S0960129516000189_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90022-0"},{"key":"S0960129516000189_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-013-9230-0"},{"key":"S0960129516000189_ref1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1049"},{"key":"S0960129516000189_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.04.003"},{"key":"S0960129516000189_ref22","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exi032"},{"key":"S0960129516000189_ref21","doi-asserted-by":"crossref","DOI":"10.1525\/9780520348097","volume-title":"A Decision Method for Elementary Algebra and Geometry","author":"Tarski","year":"1951"},{"key":"S0960129516000189_ref12","first-page":"428","volume-title":"The Continuum Companion to Philosophical Logic","author":"Paris","year":"2011"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129516000189","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T09:50:58Z","timestamp":1656755458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129516000189\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,29]]},"references-count":22,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["S0960129516000189"],"URL":"https:\/\/doi.org\/10.1017\/s0960129516000189","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,29]]}}}