{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:10:51Z","timestamp":1760202651860,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2012,11,29]],"date-time":"2012-11-29T00:00:00Z","timestamp":1354147200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Continuous Markovian Logic (CML) is a multimodal logic that expresses\nquantitative and qualitative properties of continuous-time labelled Markov\nprocesses with arbitrary (analytic) state-spaces, henceforth called continuous\nMarkov processes (CMPs). The modalities of CML evaluate the rates of the\nexponentially distributed random variables that characterize the duration of\nthe labeled transitions of a CMP. In this paper we present weak and strong\ncomplete axiomatizations for CML and prove a series of metaproperties,\nincluding the finite model property and the construction of canonical models.\nCML characterizes stochastic bisimilarity and it supports the definition of a\nquantified extension of the satisfiability relation that measures the\n\"compatibility\" between a model and a property. In this context, the\nmetaproperties allows us to prove two robustness theorems for the logic stating\nthat one can perturb formulas and maintain \"approximate satisfaction\".<\/jats:p>","DOI":"10.2168\/lmcs-8(4:19)2012","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:21:33Z","timestamp":1385731293000},"source":"Crossref","is-referenced-by-count":7,"title":["Continuous Markovian Logics - Axiomatization and Quantified Metatheory"],"prefix":"10.46298","volume":"Volume 8, Issue 4","author":[{"given":"Radu","family":"Mardare","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8705-8488","authenticated-orcid":false,"given":"Luca","family":"Cardelli","sequence":"additional","affiliation":[]},{"given":"Kim G.","family":"Larsen","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2012,11,29]]},"reference":[{"key":"733:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/937\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/937\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:59:28Z","timestamp":1681243168000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/937"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,29]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-8(4:19)2012","relation":{"is-same-as":[{"id-type":"arxiv","id":"1211.5190","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1211.5190","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1610.08169","asserted-by":"subject"},{"id-type":"doi","id":"10.4204\/eptcs.227.4","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1610.08169","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2012,11,29]]},"article-number":"937"}}