{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T13:22:19Z","timestamp":1758979339114,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T00:00:00Z","timestamp":1532044800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T00:00:00Z","timestamp":1532044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T00:00:00Z","timestamp":1532044800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-11-IDEX-0002"],"award-info":[{"award-number":["ANR-11-IDEX-0002"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-11-LABX-0040"],"award-info":[{"award-number":["ANR-11-LABX-0040"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>A dynamical system is a pair $(X,f)$, where $X$ is a topological space and $f\\colon X\\to X$ is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems, giving rise to a natural intuitionistic temporal logic. We introduce a variant of Kremer's logic, which we denote ${\\sf ITL^c}$, and show that it is decidable. We also show that minimality and Poincar\\'e recurrence are both expressible in the language of ${\\sf ITL^c}$, thus providing a decidable logic expressive enough to reason about non-trivial asymptotic behavior in dynamical systems.<\/jats:p>","DOI":"10.23638\/lmcs-14(3:3)2018","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:32:11Z","timestamp":1743701531000},"source":"Crossref","is-referenced-by-count":1,"title":["The intuitionistic temporal logic of dynamical systems"],"prefix":"10.23638","volume":"Volume 14, Issue 3","author":[{"given":"David","family":"Fern\u00e1ndez-Duque","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2018,7,20]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1611.06929v7","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1611.06929v7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:32:11Z","timestamp":1743701531000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3280"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-14(3:3)2018","relation":{"has-preprint":[{"id-type":"arxiv","id":"1611.06929v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1611.06929v4","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1611.06929","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1611.06929","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2018,7,20]]},"article-number":"3280"}}