{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T12:25:06Z","timestamp":1710332706307},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2022,5,28]],"date-time":"2022-05-28T00:00:00Z","timestamp":1653696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Department of Philosophy \u2018Piero Martinetti\u2019 of the University of Milan"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,17]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First, we identify the conditions under which propositional probability functions can be approximated by a hierarchy of depth-bounded belief functions. Second, we show that under rather palatable restrictions, our approximations of probability lead to uncertain reasoning which, under the usual assumptions in the field, qualifies as tractable.<\/jats:p>","DOI":"10.1093\/logcom\/exac038","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T19:12:30Z","timestamp":1651518750000},"page":"599-622","source":"Crossref","is-referenced-by-count":2,"title":["A logic-based tractable approximation of probability"],"prefix":"10.1093","volume":"33","author":[{"given":"Paolo","family":"Baldi","sequence":"first","affiliation":[{"name":"Department of Philosophy , University of Milan, Via Festa del Perdono 7, 20122 Milan, Italy"}]},{"given":"Hykel","family":"Hosni","sequence":"additional","affiliation":[{"name":"Department of Philosophy , University of Milan, Via Festa del Perdono 7, 20122 Milan, Italy"}]}],"member":"286","published-online":{"date-parts":[[2022,5,28]]},"reference":[{"key":"2023041803282659500_","first-page":"607","article-title":"Depth-bounded approximations of probability","volume-title":"Communications in Computer and Information Science","author":"Baldi","year":"2020"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.ijar.2020.05.001","article-title":"Depth-bounded belief functions","volume":"123","author":"Baldi","year":"2020","journal-title":"International Journal of Approximate Reasoning"},{"key":"2023041803282659500_","article-title":"Logical approximations of qualitative probability","volume-title":"Proceedings of the 12th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA)","author":"Baldi","year":"2021"},{"key":"2023041803282659500_","first-page":"39","article-title":"Generalized probabilistic satisfiability","volume":"332","author":"Caleiro","year":"2017","journal-title":"Information and Computation"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s11229-008-9409-4","article-title":"The enduring scandal of deduction","volume":"167","author":"D\u2019Agostino","year":"2009","journal-title":"Synthese"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.tcs.2015.06.057","article-title":"An informational view of classical logic","volume":"606","author":"D\u2019Agostino","year":"2015","journal-title":"Theoretical Computer Science"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.tcs.2013.02.014","article-title":"Semantics and proof-theory of depth bounded boolean logics","volume":"480","author":"D\u2019Agostino","year":"2013","journal-title":"Theoretical Computer Science"},{"key":"2023041803282659500_","first-page":"1","article-title":"Rational beliefs real agents can have\u2014A logical point of view","volume":"58","author":"D\u2019Agostino","year":"2016","journal-title":"Journal of Machine Learning Research: Workshops and Conference and Proceedings"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"298","DOI":"10.4064\/fm-17-1-298-329","article-title":"Sul significato soggettivo della probabilit\u00e0","volume":"17","author":"de Finetti","year":"1931","journal-title":"Fundamenta Mathematicae"},{"key":"2023041803282659500_","volume-title":"Theory of Probability","author":"de Finetti","year":"1974"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1023\/A:1016740830286","article-title":"Possibility theory, probability theory and multiple-valued: A clarification","volume":"32","author":"Dubois","year":"2001","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"643","DOI":"10.2307\/1884324","article-title":"Risk, ambiguity, and the Savage axioms","volume":"75","author":"Ellsberg","year":"1961","journal-title":"Quarterly Journal of Economics"},{"key":"2023041803282659500_","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":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.tcs.2006.01.007","article-title":"The universe of propositional approximations","volume":"355","author":"Finger","year":"2006","journal-title":"Theoretical Computer Science"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s10472-015-9466-6","article-title":"Probabilistic satisfiability: Algorithms with the presence and absence of a phase transition","volume":"75","author":"Finger","year":"2015","journal-title":"Annals of Mathematics and Artificial Intelligence"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-007-0008-6","volume-title":"Probabilistic Logics and Probabilistic Networks","author":"Haenni","year":"2011"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1086\/288169","article-title":"Slightly more realistic personal probability","volume":"34","author":"Hacking","year":"1967","journal-title":"Philosophy of Science"},{"key":"2023041803282659500_","volume-title":"Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications","author":"Hailperin","year":"1996"},{"key":"2023041803282659500_","volume-title":"Reasoning about Uncertainty","author":"Halpern","year":"2003"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/978-94-017-1737-3_8","article-title":"Probabilistic satisfiability","volume-title":"Handbook of Defeasible Reasoning and Uncertainty Management Systems","author":"Hansen","year":"2000"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF00159221","article-title":"Coherent bets under partially resolving uncertainty and belief functions","volume":"26","author":"Jaffray","year":"1989","journal-title":"Theory and Decision"},{"key":"2023041803282659500_","volume-title":"Treatise on Probability","author":"Keynes","year":"1921"},{"key":"2023041803282659500_","volume-title":"Risk, Uncertainty and Profit","author":"Knight","year":"1921"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511612947","volume-title":"Uncertain Inference","author":"Kyburg","year":"2001"},{"key":"2023041803282659500_","first-page":"624","article-title":"A first-order logic of limited belief based on possible worlds","volume-title":"Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning (KR 2020)","author":"Lakemeyer","year":"2020"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1402448","article-title":"Scoring rules and the inevitability of probability","volume":"50","author":"Lindley","year":"1982","journal-title":"International Statistical Review"},{"key":"2023041803282659500_","volume-title":"A Guided Tour of Artificial Intelligence Research 1: Knowledge Representation, Reasoning and Learning","author":"Marquis","year":"2020"},{"key":"2023041803282659500_","volume-title":"The Uncertain Reasoner\u2019s Companion: A Mathematical Perspective","author":"Paris","year":"1994"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1086\/288168","article-title":"Difficulties in the theory of personal probability","volume":"34","author":"Savage","year":"1967","journal-title":"Philosophy of Science"},{"key":"2023041803282659500_","volume-title":"The Foundations of Statistics","author":"Savage","year":"1972"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"571","DOI":"10.2307\/1911053","article-title":"Subjective probability and expected utility without additivity","volume":"57","author":"Schmeidler","year":"1989","journal-title":"Econometrica"},{"key":"2023041803282659500_","volume-title":"Theory of Linear and Integer Programming","author":"Schrijver","year":"1987"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","DOI":"10.1515\/9780691214696","volume-title":"A Mathematical Theory of Evidence","author":"Shafer","year":"1976"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/0888-613X(90)90012-Q","article-title":"Perspectives on the theory and practice of belief functions","volume":"4","author":"Shafer","year":"1990","journal-title":"International Journal of Approximate Reasoning"},{"key":"2023041803282659500_","volume-title":"Introduction to the Theory of Computation","author":"Sipser","year":"1997"},{"key":"2023041803282659500_","volume-title":"What Intelligence Tests Miss: The Psychology of Rational Thought","author":"Stanovich","year":"2009"},{"key":"2023041803282659500_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3472-7","volume-title":"Statistical Reasoning with Imprecise Probabilities","author":"Walley","year":"1991"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/33\/3\/599\/50001716\/exac038.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/33\/3\/599\/50001716\/exac038.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T23:19:33Z","timestamp":1700522373000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/33\/3\/599\/6593104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,28]]},"references-count":37,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,5,28]]},"published-print":{"date-parts":[[2023,4,17]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exac038","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,4]]},"published":{"date-parts":[[2022,5,28]]}}}