{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T19:20:24Z","timestamp":1648927224026},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindstr\u00f6m characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\\mathcal{F}\\mathcal{P}\\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\\mathcal{F}\\mathcal{P}\\mathcal{M}$.<\/jats:p>","DOI":"10.1093\/logcom\/exaa066","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T04:48:43Z","timestamp":1605847723000},"page":"393-415","source":"Crossref","is-referenced-by-count":0,"title":["Probability logic: A model-theoretic perspective"],"prefix":"10.1093","volume":"31","author":[{"given":"M","family":"Pourmahdian","sequence":"first","affiliation":[{"name":"School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran; Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15194, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R","family":"Zoghifard","sequence":"additional","affiliation":[{"name":"School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,12,16]]},"reference":[{"key":"2021030623535971800_ref1","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s001820050112","article-title":"Interactive epistemology ii: probability","volume":"28","author":"Aumann","year":"1999","journal-title":"International Journal of Game Theory"},{"key":"2021030623535971800_ref2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-34514-5","volume-title":"Measure Theory","author":"Bogachev","year":"2007"},{"key":"2021030623535971800_ref3","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1006\/inco.2001.2962","article-title":"Bisimulation for labelled Markov processes","volume":"179","author":"Desharnais","year":"2002","journal-title":"Information and Computation"},{"key":"2021030623535971800_ref4","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/S0890-5401(03)00051-8","article-title":"Approximating labelled Markov processes","volume":"184","author":"Desharnais","year":"2003","journal-title":"Information and Computation"},{"key":"2021030623535971800_ref5","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s11787-013-0078-9","article-title":"A general Lindstr\u00f6m theorem for some normal modal logics","volume":"7","author":"Enqvist","year":"2013","journal-title":"Logica Universalis"},{"key":"2021030623535971800_ref6","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/0890-5401(90)90060-U","article-title":"A logic for reasoning about probabilities","volume":"87","author":"Fagin","year":"1990","journal-title":"Information and Computation"},{"key":"2021030623535971800_ref7","volume-title":"Real Analysis: Modern Techniques and Their Applications","author":"Folland","year":"2013"},{"key":"2021030623535971800_ref8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511542725","volume-title":"Continuous Lattices and Domains","author":"Gierz","year":"2003"},{"key":"2021030623535971800_ref9","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1093\/logcom\/exn092","article-title":"Deduction systems for coalgebras over measurable spaces","volume":"20","author":"Goldblatt","year":"2010","journal-title":"Journal of Logic and Computation"},{"key":"2021030623535971800_ref10","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1287\/mnsc.14.5.320","article-title":"Games with incomplete information played by Bayesian players part ii. 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