{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:21Z","timestamp":1753894401849,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper, we prove measurability of event for which a general\ncontinuous-time stochastic process satisfies continuous-time Metric Temporal\nLogic (MTL) formula. Continuous-time MTL can define temporal constrains for\nphysical system in natural way. Then there are several researches that deal\nwith probability of continuous MTL semantics for stochastic processes. However,\nproving measurability for such events is by no means an obvious task, even\nthough it is essential. The difficulty comes from the semantics of \"until\noperator\", which is defined by logical sum of uncountably many propositions.\nGiven the difficulty involved in proving the measurability of such an event\nusing classical measure-theoretic methods, we employ a theorem from stochastic\nanalysis. This theorem is utilized to prove the measurability of hitting times\nfor stochastic processes, and it stands as a profound result within the theory\nof capacity. Next, we provide an example that illustrates the failure of\nprobability approximation when discretizing the continuous semantics of MTL\nformulas with respect to time. Additionally, we prove that the probability of\nthe discretized semantics converges to that of the continuous semantics when we\nimpose restrictions on diamond operators to prevent nesting.<\/jats:p>","DOI":"10.46298\/lmcs-20(2:14)2024","type":"journal-article","created":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T08:15:12Z","timestamp":1718266512000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Metric Temporal Logic for Continuous Stochastic Processes"],"prefix":"10.46298","volume":"Volume 20, Issue 2","author":[{"given":"Mitsumasa","family":"Ikeda","sequence":"first","affiliation":[]},{"given":"Yoriyuki","family":"Yamagata","sequence":"additional","affiliation":[]},{"given":"Takayuki","family":"Kihara","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,6,13]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13774\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13774\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T08:15:12Z","timestamp":1718266512000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11692"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,13]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(2:14)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2308.00984v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2308.00984v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2308.00984","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2308.00984","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,6,13]]},"article-number":"11692"}}