{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T05:22:42Z","timestamp":1776316962272,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We study an extension of modal $\\mu$-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becomes undecidable. We also show expressive limitations of atom-enriched $\\mu$-calculi, and explain how their expressive power depends on the structure of atoms used, and on the choice between basic or vectorial syntax.<\/jats:p>","DOI":"10.23638\/lmcs-15(4:5)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:14Z","timestamp":1743701834000},"source":"Crossref","is-referenced-by-count":1,"title":["Scalar and Vectorial mu-calculus with Atoms"],"prefix":"10.23638","volume":"Volume 15, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5793-7425","authenticated-orcid":false,"given":"Bartek","family":"Klin","sequence":"first","affiliation":[]},{"given":"Mateusz","family":"\u0141e\u0142yk","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,10,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1803.06752v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1803.06752v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:37:14Z","timestamp":1743701834000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4389"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(4:5)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1803.06752v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1803.06752v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1803.06752","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1803.06752","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,29]]},"article-number":"4389"}}