{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:11Z","timestamp":1753889771272,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2012,9,12]],"date-time":"2012-09-12T00:00:00Z","timestamp":1347408000000},"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>Coalgebras for a functor model different types of transition systems in a\nuniform way. This paper focuses on a uniform account of finitary logics for\nset-based coalgebras. In particular, a general construction of a logic from an\narbitrary set-functor is given and proven to be strongly complete under\nadditional assumptions. We proceed in three parts. Part I argues that sifted\ncolimit preserving functors are those functors that preserve universal\nalgebraic structure. Our main theorem here states that a functor preserves\nsifted colimits if and only if it has a finitary presentation by operations and\nequations. Moreover, the presentation of the category of algebras for the\nfunctor is obtained compositionally from the presentations of the underlying\ncategory and of the functor. Part II investigates algebras for a functor over\nind-completions and extends the theorem of J{\\'o}nsson and Tarski on canonical\nextensions of Boolean algebras with operators to this setting. Part III shows,\nbased on Part I, how to associate a finitary logic to any finite-sets\npreserving functor T. Based on Part II we prove the logic to be strongly\ncomplete under a reasonable condition on T.<\/jats:p>","DOI":"10.2168\/lmcs-8(3:14)2012","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T08:17:46Z","timestamp":1385713066000},"source":"Crossref","is-referenced-by-count":8,"title":["Strongly Complete Logics for Coalgebras"],"prefix":"10.46298","volume":"Volume 8, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8685-5207","authenticated-orcid":false,"given":"Alexander","family":"Kurz","sequence":"first","affiliation":[]},{"given":"Jiri","family":"Rosicky","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2012,9,12]]},"reference":[{"key":"150:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1231\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1231\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:06:14Z","timestamp":1681243574000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,12]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-8(3:14)2012","relation":{"is-same-as":[{"id-type":"arxiv","id":"1207.2732","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1207.2732","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2012,9,12]]},"article-number":"1231"}}