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Besides the standard knowledge modalities, our logic provides additional agent-specific hope modalities capable of expressing that an agent is not faulty, and also dynamic modalities enabling change to the agents\u2019 correctness status. These dynamic modalities are interpreted as model updates that come in three flavors: fully public, more private, and\/or involving factual change. Tailored examples demonstrate the utility and flexibility of our logic for modeling a wide range of fault-detection, isolation, and recovery (FDIR) approaches in mission-critical distributed systems. By providing complete axiomatizations for all variants of our logic, we also create a foundation for building future verification tools for this important class of fault-tolerant applications.<\/jats:p>","DOI":"10.1007\/978-3-031-63501-4_7","type":"book-chapter","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T09:02:00Z","timestamp":1719824520000},"page":"114-134","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Logic for\u00a0Repair and\u00a0State Recovery in\u00a0Byzantine Fault-Tolerant Multi-agent Systems"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4526-8687","authenticated-orcid":false,"given":"Hans","family":"van Ditmarsch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2013-1003","authenticated-orcid":false,"given":"Krisztina","family":"Fruzsa","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9831-8583","authenticated-orcid":false,"given":"Ulrich","family":"Schmid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,2]]},"reference":[{"key":"7_CR1","doi-asserted-by":"publisher","unstructured":"Adams, J.C., Ramarao, K.V.S.: Distributed diagnosis of byzantine processors and links. 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