{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:23Z","timestamp":1753894343394,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"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>Using the theory of coalgebra, we introduce a uniform framework for adding\nmodalities to the language of propositional geometric logic. Models for this\nlogic are based on coalgebras for an endofunctor on some full subcategory of\nthe category of topological spaces and continuous functions. We investigate\nderivation systems, soundness and completeness for such geometric modal logics,\nand we specify a method of lifting an endofunctor on Set, accompanied by a\ncollection of predicate liftings, to an endofunctor on the category of\ntopological spaces, again accompanied by a collection of (open) predicate\nliftings. Furthermore, we compare the notions of modal equivalence, behavioural\nequivalence and bisimulation on the resulting class of models, and we provide a\nfinal object for the corresponding category.<\/jats:p>","DOI":"10.46298\/lmcs-18(4:10)2022","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T09:46:02Z","timestamp":1672134362000},"source":"Crossref","is-referenced-by-count":0,"title":["Coalgebraic Geometric Logic: Basic Theory"],"prefix":"10.46298","volume":"Volume 18, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6692-5051","authenticated-orcid":false,"given":"Nick","family":"Bezhanishvili","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jim","family":"de Groot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yde","family":"Venema","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,12,8]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/10441\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/10441\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:17:40Z","timestamp":1687292260000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/6205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,8]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(4:10)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"1903.08837v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1903.08837v4","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1903.08837","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1903.08837","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,12,8]]},"article-number":"6205"}}