{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T18:33:52Z","timestamp":1768070032702,"version":"3.49.0"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2017,4,8]],"date-time":"2017-04-08T00:00:00Z","timestamp":1491609600000},"content-version":"unspecified","delay-in-days":1680,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2012,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Dynamic Topological Logic (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000578_inline01\"\/>) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000578_inline01\"\/> over the class of all dynamical systems has proven to be quite elusive.<\/jats:p><jats:p>Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different context. We then provide a sound axiomatization for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200000578_inline01\"\/> over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof.<\/jats:p>","DOI":"10.2178\/jsl\/1344862169","type":"journal-article","created":{"date-parts":[[2012,11,5]],"date-time":"2012-11-05T10:02:32Z","timestamp":1352109752000},"page":"947-969","source":"Crossref","is-referenced-by-count":11,"title":["A sound and complete axiomatization for Dynamic Topological Logic"],"prefix":"10.1017","volume":"77","author":[{"given":"David","family":"Fern\u00e1ndez-Duque","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2017,4,8]]},"reference":[{"key":"S0022481200000578_ref024","doi-asserted-by":"publisher","DOI":"10.4064\/fm-31-1-103-134"},{"key":"S0022481200000578_ref022","first-page":"46","volume-title":"Proceedings 18th IEEE symposium on the foundations of computer science","author":"Pnueli","year":"1977"},{"key":"S0022481200000578_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-005-0285-z"},{"key":"S0022481200000578_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.12.018"},{"key":"S0022481200000578_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-4648-6"},{"key":"S0022481200000578_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.06.003"},{"key":"S0022481200000578_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-9005-x"},{"key":"S0022481200000578_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.01.015"},{"key":"S0022481200000578_ref006","first-page":"100","volume-title":"Advances in modal logic","author":"Fern\u00e1ndez-Duque","year":"2010"},{"key":"S0022481200000578_ref023","volume-title":"Time and modality","author":"Prior","year":"1957"},{"key":"S0022481200000578_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2008.09.015"},{"key":"S0022481200000578_ref020","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/8.1.55"},{"key":"S0022481200000578_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-011-9339-x"},{"key":"S0022481200000578_ref019","article-title":"Completeness of S4 for the Lebesgue measure algebra","author":"Lando","year":"2010","journal-title":"Journal of Philosophical Logic"},{"key":"S0022481200000578_ref009","first-page":"857","volume-title":"Proceedings of IJCAI","author":"Fern\u00e1ndez-Duque","year":"2011"},{"key":"S0022481200000578_ref010","first-page":"308","volume":"77","author":"Fern\u00e1ndez-Duque","year":"2012","journal-title":"Dynamic topological logic interpreted over metric spaces"},{"key":"S0022481200000578_ref018","volume-title":"Many-dimensional modal logics: Theory and applications","volume":"148","author":"Kurucz","year":"2003"},{"key":"S0022481200000578_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2009.04.002"},{"key":"S0022481200000578_ref013","first-page":"299","volume-title":"Advances in modal logic","volume":"6","author":"Konev","year":"2006"},{"key":"S0022481200000578_ref001","doi-asserted-by":"publisher","DOI":"10.21236\/ADA344355"},{"key":"S0022481200000578_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-010-9160-4"},{"key":"S0022481200000578_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2006.01.001"},{"key":"S0022481200000578_ref016","unstructured":"Kremer P. , Strong completeness of SA wrt the real line, 2012."},{"key":"S0022481200000578_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.06.004"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200000578","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,24]],"date-time":"2019-04-24T19:28:56Z","timestamp":1556134136000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200000578\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["S0022481200000578"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1344862169","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,9]]}}}