{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T11:33:49Z","timestamp":1648812829966},"reference-count":14,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T00:00:00Z","timestamp":1603843200000},"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":[[2022,1,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Dynamic topological logic ($\\textsf{DTL}$) is a multi-modal logic that was introduced for reasoning about dynamic topological systems, i.e. structures of the form $\\langle{\\mathfrak{X}, f}\\rangle $, where $\\mathfrak{X}$ is a topological space and $f$ is a continuous function on it. The problem of finding a complete and natural axiomatization for this logic in the original tri-modal language has been open for more than one decade. In this paper, we give a natural axiomatization of $\\textsf{DTL}$ and prove its strong completeness with respect to the class of all dynamic topological systems. Our proof system is infinitary in the sense that it contains an infinitary derivation rule with countably many premises and one conclusion. It should be remarked that $\\textsf{DTL}$ is semantically non-compact, so no finitary proof system for this logic could be strongly complete. Moreover, we provide an infinitary axiomatic system for the logic ${\\textsf{DTL}}_{\\mathcal{A}}$, i.e. the $\\textsf{DTL}$ of Alexandrov spaces, and show that it is strongly complete with respect to the class of all dynamical systems based on Alexandrov spaces.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa055","type":"journal-article","created":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T03:31:12Z","timestamp":1601004672000},"page":"124-142","source":"Crossref","is-referenced-by-count":0,"title":["An infinitary axiomatization of dynamic topological logic"],"prefix":"10.1093","volume":"30","author":[{"given":"Somayeh","family":"Chopoghloo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran 1983969411, Iran"}]},{"given":"Morteza","family":"Moniri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran 1983969411, Iran"}]}],"member":"286","published-online":{"date-parts":[[2020,10,28]]},"reference":[{"key":"2022011721343068100_ref1","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1093\/logcom\/13.6.889","article-title":"Reasoning about space: the modal way","volume":"13","author":"Aiello","year":"2003","journal-title":"Journal Logic and Computation"},{"key":"2022011721343068100_ref2","first-page":"97","article-title":"Modal logics and topological semantics for hybrid system","author":"Artemov","year":"1997","journal-title":"Technical Report MSI"},{"key":"2022011721343068100_ref3","doi-asserted-by":"crossref","first-page":"30","DOI":"10.2307\/2266324","article-title":"On axiomatizability within a system","volume":"18","author":"Craig","year":"1953","journal-title":"Journal of Symbolic Logic"},{"key":"2022011721343068100_ref4","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.apal.2008.09.015","article-title":"Non-deterministic semantics for dynamic 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Information"},{"key":"2022011721343068100_ref13","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF01048686","article-title":"A model existence theorem in infinitary propositional modal logic","volume":"23","author":"Segerberg","year":"1994","journal-title":"Journal of Philosophical Logic"},{"key":"2022011721343068100_ref14","doi-asserted-by":"crossref","first-page":"103","DOI":"10.4064\/fm-31-1-103-134","article-title":"Der Aussagenkalk\u00fcl und die topologie","volume":"31","author":"Tarski","year":"1938","journal-title":"Fundamenta Mathematica"}],"container-title":["Logic Journal of the 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