{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T21:09:09Z","timestamp":1776373749240,"version":"3.51.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,6,24]]},"abstract":"<jats:p>Closure spaces, a generalisation of topological spaces, have shown to be a convenient theoretical framework for spatial model checking. The closure operator of closure spaces and quasi-discrete closure spaces induces a notion of neighborhood akin to that of topological spaces that build on open sets. For closure models and quasi-discrete closure models, in this paper we present three notions of bisimilarity that are logically characterised by corresponding modal logics with spatial modalities: (i) CM-bisimilarity for closure models (CMs) is shown to generalise topo-bisimilarity for topological models and to be an instantiation of neighbourhood bisimilarity, when CMs are seen as (augmented) neighbourhood models. CM-bisimilarity corresponds to equivalence with respect to the infinitary modal logic IML that includes the modality ${\\cal N}$ for ``being near to''. (ii) CMC-bisimilarity, with `CMC' standing for CM-bisimilarity with converse, refines CM-bisimilarity for quasi-discrete closure spaces, carriers of quasi-discrete closure models. Quasi-discrete closure models come equipped with two closure operators, Direct ${\\cal C}$ and Converse ${\\cal C}$, stemming from the binary relation underlying closure and its converse. CMC-bisimilarity, is captured by the infinitary modal logic IMLC including two modalities, Direct ${\\cal N}$ and Converse ${\\cal N}$, corresponding to the two closure operators. (iii) CoPa-bisimilarity on quasi-discrete closure models, which is weaker than CMC-bisimilarity, is based on the notion of compatible paths. The logical counterpart of CoPa-bisimilarity is the infinitary modal logic ICRL with modalities Direct $\u03b6$ and Converse $\u03b6$, whose semantics relies on forward and backward paths, respectively. It is shown that CoPa-bisimilarity for quasi-discrete closure models relates to divergence-blind stuttering equivalence for Kripke models.<\/jats:p>","DOI":"10.46298\/lmcs-21(3:21)2025","type":"journal-article","created":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T10:25:08Z","timestamp":1756203908000},"source":"Crossref","is-referenced-by-count":1,"title":["On Bisimilarity for Quasi-discrete Closure Spaces"],"prefix":"10.46298","volume":"Volume 21, Issue 3","author":[{"given":"Vincenzo","family":"Ciancia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Diego","family":"Latella","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mieke","family":"Massink","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik P.","family":"de Vink","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,8,26]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2301.11634v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2301.11634v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T10:25:08Z","timestamp":1756203908000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10873"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,26]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(3:21)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2301.11634v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2301.11634v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2301.11634v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2301.11634","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2301.11634","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,26]]},"article-number":"10873"}}