{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:24:12Z","timestamp":1770899052250,"version":"3.50.1"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2020,12,28]],"date-time":"2020-12-28T00:00:00Z","timestamp":1609113600000},"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":[[2021,12,22]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group belief under different assumptions about the properties of belief. In particular, we map out (lack of) preservation of belief properties against different standard definitions of group belief. It turns out that what is called group belief most often is not actually belief, i.e. does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, neither common belief (does not satisfy the negative introspection axiom 5) nor distributed belief (does not satisfy the consistency axiom D) are not actually belief. There has been some confusion in the literature regarding soundness of proposed axiomatizations of logics with distributed knowledge, related to the mentioned lack of preservation. In this paper we also present detailed completeness proofs of sound and complete axiomatizations of KD45 with distributed belief, both with and without common belief.<\/jats:p>","DOI":"10.1093\/logcom\/exaa068","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T18:37:10Z","timestamp":1605897430000},"page":"1959-1978","source":"Crossref","is-referenced-by-count":5,"title":["Group belief"],"prefix":"10.1093","volume":"31","author":[{"given":"Thomas","family":"\u00c5gotnes","sequence":"first","affiliation":[{"name":"Institute of Logic and Intelligence, Southwest University, Chongqing 400715, China and Department of Information Science and Media Studies, University of Bergen, N-5020 Bergen, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y\u00ec N","family":"W\u00e1ng","sequence":"additional","affiliation":[{"name":"Department of Philosophy (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,12,28]]},"reference":[{"key":"2021121717364400800_ref1","article-title":"What no one knows","volume-title":"10th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2012)","author":"Agotnes","year":"2012"},{"key":"2021121717364400800_ref2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.artint.2017.07.002","article-title":"Resolving distributed knowledge","volume":"252","author":"Agotnes","year":"2017","journal-title":"Artificial Intelligence"},{"key":"2021121717364400800_ref3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-030-44638-3_1","article-title":"Group belief","volume-title":"Logic and Argumentation","author":"Agotnes","year":"2020"},{"key":"2021121717364400800_ref4","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/978-3-7908-1888-8_17","article-title":"Axiomatization of logics based on kripke models with relative accessibility relations","volume-title":"Incomplete Information: Rough Set Analysis","author":"Balbiani","year":"1998"},{"key":"2021121717364400800_ref5","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/978-3-319-62864-6_5","article-title":"Group knowledge in interrogative epistemology","volume-title":"Jaakko Hintikka on Knowledge and Game-Theoretical Semantics","author":"Baltag","year":"2018"},{"key":"2021121717364400800_ref6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10992-018-9463-4","article-title":"A topological approach to full belief","volume":"48","author":"Baltag","year":"2019","journal-title":"Journal of Philosophical Logic"},{"key":"2021121717364400800_ref7","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1007\/978-3-319-20451-2_39","article-title":"A qualitative theory of dynamic interactive belief revision","volume-title":"Readings in Formal Epistemology: Sourcebook","author":"Baltag","year":"2016"},{"key":"2021121717364400800_ref8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","article-title":"Modal logic","volume-title":"Cambridge Tracts in Theoretical Computer Science","author":"Blackburn","year":"2001"},{"key":"2021121717364400800_ref9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.artint.2017.01.001","article-title":"Graph aggregation","volume":"245","author":"Endriss","year":"2017","journal-title":"Artificial Intelligence"},{"key":"2021121717364400800_ref10","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1145\/174652.174658","article-title":"Reasoning about knowledge and probability","volume":"41","author":"Fagin","year":"1994","journal-title":"Journal of the ACM"},{"key":"2021121717364400800_ref11","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/5803.001.0001","volume-title":"Reasoning About Knowledge","author":"Fagin","year":"1995"},{"key":"2021121717364400800_ref12","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0168-0072(98)00033-5","article-title":"Common knowledge revisited","volume":"96","author":"Fagin","year":"1999","journal-title":"Annals of Pure and Applied Logic"},{"key":"2021121717364400800_ref13","volume-title":"Reasoning About Knowledge","author":"Fagin","year":"2003"},{"key":"2021121717364400800_ref14","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1145\/128749.150945","article-title":"What can machines know? 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