{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:38:46Z","timestamp":1740141526494,"version":"3.37.3"},"reference-count":49,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2020,7,21]],"date-time":"2020-07-21T00:00:00Z","timestamp":1595289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100002808","name":"Carlsberg Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002808","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Collective Attitude Formation","award":["RO 4548\/8-1"],"award-info":[{"award-number":["RO 4548\/8-1"]}]},{"name":"Shared Evidence to Group Attitudes","award":["RO 4548\/6-1"],"award-info":[{"award-number":["RO 4548\/6-1"]}]},{"name":"Foundations, Applications and Theory of Inductive Logic","award":["432308570"],"award-info":[{"award-number":["432308570"]}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["17ZDA026"],"award-info":[{"award-number":["17ZDA026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper analyses dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the Stone topology, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behaviour of said maps. Among the recurrence results, we show maps induced by finite action models may have uncountably many recurrent points, even when initiated on a finite input model. Several recurrence results draws on the class of action models being Turing complete, for which the paper provides proof in the postcondition-free case. As upper bounds, it is shown that either 1 atom, 3 agents and preconditions of modal depth 18 or 1 atom, 7 agents and preconditions of modal depth 3 suffice for Turing completeness.<\/jats:p>","DOI":"10.1093\/logcom\/exaa035","type":"journal-article","created":{"date-parts":[[2020,6,5]],"date-time":"2020-06-05T19:26:52Z","timestamp":1591385212000},"page":"1213-1238","source":"Crossref","is-referenced-by-count":3,"title":["Convergence, continuity, recurrence and Turing completeness in dynamic epistemic logic1"],"prefix":"10.1093","volume":"30","author":[{"given":"Dominik","family":"Klein","sequence":"first","affiliation":[{"name":"Department of Philosophy, Bayreuth University, 95447 Bayreuth, Germany and Department of Political Science, University of Bamberg, 96047 Bamberg, Germany"}]},{"given":"Rasmus K","family":"Rendsvig","sequence":"additional","affiliation":[{"name":"Center for Information and Bubble Studies, University of Copenhagen, 2300 Copenhagen, Denmark"}]}],"member":"286","published-online":{"date-parts":[[2020,7,21]]},"reference":[{"key":"2020081904465237600_ref1","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1093\/jigpal\/jzp037","article-title":"Generalizing AGM to a multi-agent setting","volume":"18","author":"Aucher","year":"2010","journal-title":"Logic Journal of IGPL"},{"key":"2020081904465237600_ref2","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1023\/B:SYNT.0000024912.56773.5e","article-title":"Logics for epistemic programs","volume":"139","author":"Baltag","year":"2004","journal-title":"Synthese"},{"key":"2020081904465237600_ref3","article-title":"The logic of public announcements, common knowledge, and private suspicions","volume-title":"TARK 1998","author":"Baltag","year":"1998"},{"key":"2020081904465237600_ref4","article-title":"Dynamic epistemic logic","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Baltag","year":"2016"},{"key":"2020081904465237600_ref5","article-title":"A qualitative theory of dynamic interactive belief revision","volume-title":"Proc. LOFT 7","author":"Baltag","year":"2008"},{"key":"2020081904465237600_ref6","doi-asserted-by":"crossref","DOI":"10.1145\/1562814.1562824","article-title":"Group belief dynamics under iterated revision: fixed points and cycles of joint upgrades","volume-title":"TARK\u201909","author":"Baltag","year":"2009"},{"key":"2020081904465237600_ref7","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1111\/1467-8586.00133","article-title":"Games in dynamic-epistemic logic","volume":"53","author":"van Benthem","year":"2001","journal-title":"Bulletin of Economic Research"},{"key":"2020081904465237600_ref8","article-title":"One is a lonely number: logic and communication","volume-title":"Logic Colloquium \u201902","author":"van Benthem","year":"2006"},{"key":"2020081904465237600_ref9","doi-asserted-by":"crossref","first-page":"129","DOI":"10.3166\/jancl.17.129-155","article-title":"Dynamic logic for belief revision","volume":"17","author":"van Benthem","year":"2007","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2020081904465237600_ref10","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511974533","volume-title":"Logical Dynamics of Information and Interaction","author":"van Benthem","year":"2011"},{"key":"2020081904465237600_ref11","article-title":"Oscillations, logic, and dynamical systems","volume-title":"The Facts Matter","author":"van Benthem","year":"2016"},{"key":"2020081904465237600_ref12","doi-asserted-by":"crossref","first-page":"1620","DOI":"10.1016\/j.ic.2006.04.006","article-title":"Logics of communication and change","volume":"204","author":"van Benthem","year":"2006","journal-title":"Information and Computation"},{"key":"2020081904465237600_ref13","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/s10992-008-9099-x","article-title":"Merging frameworks for interaction","volume":"38","author":"van Benthem","year":"2009","journal-title":"Journal of Philosophical Logic"},{"key":"2020081904465237600_ref14","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"Blackburn","year":"2001"},{"key":"2020081904465237600_ref15","doi-asserted-by":"crossref","first-page":"9","DOI":"10.3166\/jancl.21.9-34","article-title":"Epistemic planning for single- and multi-agent systems","volume":"21","author":"Bolander","year":"2011","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"2020081904465237600_ref16","article-title":"Complexity results in epistemic planning","volume-title":"Proc. IJCAI 2015","author":"Bolander","year":"2015"},{"key":"2020081904465237600_ref17","article-title":"On distances between KD45n Kripke models and their use for belief revision","volume-title":"ECAI 2016","author":"Caridroit","year":"2016"},{"volume-title":"The Temporal Mind: Observations on the Logic of Belief Change in Interactive Systems","year":"2010","author":"D\u00e9gremont","key":"2020081904465237600_ref18"},{"key":"2020081904465237600_ref19","article-title":"Semantic results for ontic and epistemic change","volume-title":"Logic and the Foundations of Game and Decision Theory (LOFT 7)","author":"van Ditmarsch","year":"2008"},{"key":"2020081904465237600_ref20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-5839-4","volume-title":"Dynamic Epistemic Logic","author":"van Ditmarsch","year":"2008"},{"key":"2020081904465237600_ref21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-16898-2","volume-title":"Operator Theoretic Aspects of Ergodic Theory","author":"Eisner","year":"2015"},{"key":"2020081904465237600_ref22","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/5803.001.0001","volume-title":"Reasoning About Knowledge","author":"Fagin","year":"1995"},{"key":"2020081904465237600_ref23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2178\/jsl\/1344862169","article-title":"A sound and complete axiomatization for dynamic topological logic","volume":"77","author":"Fern\u00e1ndez-Duque","year":"2012","journal-title":"Journal of Symbolic Logic"},{"key":"2020081904465237600_ref24","doi-asserted-by":"crossref","first-page":"308","DOI":"10.2178\/jsl\/1327068705","article-title":"Dynamic topological logic of metric spaces","volume":"77","author":"Fern\u00e1ndez-Duque","year":"2012","journal-title":"Journal of Symbolic Logic"},{"key":"2020081904465237600_ref25","article-title":"General dynamic dynamic logic","volume-title":"Advances in Modal Logics","author":"Girard","year":"2012"},{"key":"2020081904465237600_ref26","article-title":"Model theory of modal logic","volume-title":"Handbook of Modal Logic","author":"Goranko","year":"2008"},{"key":"2020081904465237600_ref27","article-title":"Logical topologies and semantic completeness","volume-title":"Logic Colloquium\u201999","author":"Goranko","year":"2004"},{"key":"2020081904465237600_ref28","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1145\/79147.79161","article-title":"Knowledge and common knowledge in a distributed environment","volume":"37","author":"Halpern","year":"1990","journal-title":"Journal of the ACM"},{"key":"2020081904465237600_ref29","article-title":"Principal structures","volume-title":"Handbook of Dynamical Systems","author":"Hasselblatt","year":"2002"},{"volume-title":"Knowledge and Belief: An Introduction to the Logic of the Two Notions","year":"1962","author":"Hintikka","key":"2020081904465237600_ref30"},{"key":"2020081904465237600_ref31","article-title":"Cambridge Studies in Advanced Mathematics","volume-title":"Stone Spaces","author":"Johnstone","year":"1982"},{"key":"2020081904465237600_ref32","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-55665-8_8","article-title":"Convergence, continuity, and recurrence in dynamic epistemic logic","volume-title":"Logic, Rationality, and Interaction (LORI 2017, Sapporo)","author":"Klein","year":"2017"},{"article-title":"Metrics for formal structures, with an application to dynamic epistemic logic","year":"2017","author":"Klein","key":"2020081904465237600_ref33"},{"key":"2020081904465237600_ref34","first-page":"1741","article-title":"Converging on common knowledge","volume-title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI-19","author":"Klein","year":"2019"},{"key":"2020081904465237600_ref35","doi-asserted-by":"crossref","DOI":"10.1145\/2000378.2000403","article-title":"Generalized arrow update logic","volume-title":"TARK 2011, New York, NY, USA","author":"Kooi","year":"2011"},{"key":"2020081904465237600_ref36","first-page":"371","article-title":"Dynamical topological logic","volume":"3","author":"Kremer","year":"1997","journal-title":"Bulletin of Symbolic Logic"},{"key":"2020081904465237600_ref37","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-5587-4_10","article-title":"Dynamic topological logic","volume-title":"Handbook of Spatial Logics","author":"Kremer","year":"2007"},{"key":"2020081904465237600_ref38","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511626302","volume-title":"An Introduction to Symbolic Dynamics and Coding","author":"Lind","year":"1995"},{"volume-title":"Topology","year":"2000","author":"Munkres","key":"2020081904465237600_ref39"},{"key":"2020081904465237600_ref40","article-title":"Logics of public communications","volume-title":"Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems","author":"Plaza","year":"1989"},{"volume-title":"Towards a Theory of Semantic Competence","year":"2011","author":"Rendsvig","key":"2020081904465237600_ref41"},{"key":"2020081904465237600_ref42","article-title":"Diffusion, influence, and best-response dynamics in networks: an action model approach","volume-title":"Proc. ESSLLI 2014 Stud","author":"Rendsvig","year":"2014"},{"key":"2020081904465237600_ref43","doi-asserted-by":"crossref","first-page":"2471","DOI":"10.1007\/s11229-014-0435-0","article-title":"Pluralistic ignorance in the bystander effect: informational dynamics of unresponsive witnesses in situations calling for intervention","volume":"191","author":"Rendsvig","year":"2014","journal-title":"Synthese"},{"key":"2020081904465237600_ref44","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-48561-3_26","article-title":"Model transformers for dynamical systems of dynamic epistemic logic","volume-title":"Logic, Rationality, and Interaction","author":"Rendsvig","year":"2015"},{"volume-title":"Logical Dynamics and Dynamical Systems","year":"2018","author":"Rendsvig","key":"2020081904465237600_ref45"},{"key":"2020081904465237600_ref46","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0304-3975(96)00077-1","article-title":"Small universal turing machines","volume":"168","author":"Rogozhin","year":"1996","journal-title":"Theoretical Computer Science"},{"article-title":"Exploring the iterated update universe","year":"2006","author":"Sadzik","key":"2020081904465237600_ref47"},{"key":"2020081904465237600_ref48","first-page":"37","article-title":"The theory of representation for Boolean algebras","volume":"40","author":"Stone","year":"1936","journal-title":"Transactions of the American Mathematical Society"},{"key":"2020081904465237600_ref49","doi-asserted-by":"crossref","DOI":"10.1515\/9783110342406","volume-title":"Topological Dynamical Systems","author":"de Vries","year":"2014"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/6\/1213\/33663153\/exaa035.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/6\/1213\/33663153\/exaa035.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T01:21:58Z","timestamp":1722993718000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/30\/6\/1213\/5874118"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,21]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,7,21]]},"published-print":{"date-parts":[[2020,9,4]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaa035","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2020,7,21]]}}}