{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:09Z","timestamp":1753894389352,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T00:00:00Z","timestamp":1660003200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We present a finitary version of Moss' coalgebraic logic for $T$-coalgebras,\nwhere $T$ is a locally monotone endofunctor of the category of posets and\nmonotone maps. The logic uses a single cover modality whose arity is given by\nthe least finitary subfunctor of the dual of the coalgebra functor\n$T_\\omega^\\partial$, and the semantics of the modality is given by relation\nlifting. For the semantics to work, $T$ is required to preserve exact squares.\nFor the finitary setting to work, $T_\\omega^\\partial$ is required to preserve\nfinite intersections. We develop a notion of a base for subobjects of $T_\\omega\nX$. This in particular allows us to talk about the finite poset of subformulas\nfor a given formula. The notion of a base is introduced generally for a\ncategory equipped with a suitable factorisation system.\n  We prove that the resulting logic has the Hennessy-Milner property for the\nnotion of similarity based on the notion of relation lifting. We define a\nsequent proof system for the logic, and prove its completeness.<\/jats:p>","DOI":"10.46298\/lmcs-18(3:18)2022","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T07:31:32Z","timestamp":1660721492000},"source":"Crossref","is-referenced-by-count":0,"title":["Moss' logic for ordered coalgebras"],"prefix":"10.46298","volume":"Volume 18, Issue 3","author":[{"given":"Marta","family":"B\u00edlkov\u00e1","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mat\u011bj","family":"Dost\u00e1l","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,8,9]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/9902\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/9902\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:17:13Z","timestamp":1687292233000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/5158"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(3:18)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"1901.06547v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1901.06547v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1901.06547","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1901.06547","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,8,9]]},"article-number":"5158"}}