{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:18Z","timestamp":1753894398856,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T00:00:00Z","timestamp":1697587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Combinatorial topology is used in distributed computing to model concurrency\nand asynchrony. The basic structure in combinatorial topology is the simplicial\ncomplex, a collection of subsets called simplices of a set of vertices, closed\nunder containment. Pure simplicial complexes describe message passing in\nasynchronous systems where all processes (agents) are alive, whereas impure\nsimplicial complexes describe message passing in synchronous systems where\nprocesses may be dead (have crashed). Properties of impure simplicial complexes\ncan be described in a three-valued multi-agent epistemic logic where the third\nvalue represents formulae that are undefined, e.g., the knowledge and local\npropositions of dead agents. In this work we present an axiomatization for the\nlogic of the class of impure complexes and show soundness and completeness. The\ncompleteness proof involves the novel construction of the canonical simplicial\nmodel and requires a careful manipulation of undefined formulae.<\/jats:p>","DOI":"10.46298\/lmcs-19(4:3)2023","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T06:55:06Z","timestamp":1697612106000},"source":"Crossref","is-referenced-by-count":2,"title":["Impure Simplicial Complexes: Complete Axiomatization"],"prefix":"10.46298","volume":"Volume 19, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4553-5450","authenticated-orcid":false,"given":"Rojo","family":"Randrianomentsoa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4526-8687","authenticated-orcid":false,"given":"Hans","family":"van Ditmarsch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5894-8724","authenticated-orcid":false,"given":"Roman","family":"Kuznets","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2023,10,18]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/12430\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/12430\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T15:10:09Z","timestamp":1709133009000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,18]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-19(4:3)2023","relation":{"has-preprint":[{"id-type":"arxiv","id":"2211.13543v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2211.13543v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2211.13543","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2211.13543","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2023,10,18]]},"article-number":"10379"}}