{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T13:30:15Z","timestamp":1770384615554,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"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>Topological Spatial Model Checking is a recent paradigm where model checking\ntechniques are developed for the topological interpretation of Modal Logic. The\nSpatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability\nconnectives that, in turn, can be used for expressing interesting spatial\nproperties, such as \"being near to\" or \"being surrounded by\". SLCS constitutes\nthe kernel of a solid logical framework for reasoning about discrete space,\nsuch as graphs and digital images, interpreted as quasi discrete closure\nspaces. Following a recently developed geometric semantics of Modal Logic, we\npropose an interpretation of SLCS in continuous space, admitting a geometric\nspatial model checking procedure, by resorting to models based on polyhedra.\nSuch representations of space are increasingly relevant in many domains of\napplication, due to recent developments of 3D scanning and visualisation\ntechniques that exploit mesh processing. We introduce PolyLogicA, a geometric\nspatial model checker for SLCS formulas on polyhedra and demonstrate\nfeasibility of our approach on two 3D polyhedral models of realistic size.\nFinally, we introduce a geometric definition of bisimilarity, proving that it\ncharacterises logical equivalence.<\/jats:p>","DOI":"10.46298\/lmcs-18(4:7)2022","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T14:52:35Z","timestamp":1669387955000},"source":"Crossref","is-referenced-by-count":10,"title":["Geometric Model Checking of Continuous Space"],"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":"Vincenzo","family":"Ciancia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Gabelaia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gianluca","family":"Grilletti","sequence":"additional","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"}]}],"member":"25203","published-online":{"date-parts":[[2022,11,22]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/10348\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/10348\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:20:43Z","timestamp":1687292443000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9060"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,22]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(4:7)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2105.06194v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2105.06194v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2105.06194","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2105.06194","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,22]]},"article-number":"9060"}}