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These agents can operate on shared or local epistemic states through actions that dynamically alter the knowledge of some or all members of the ensemble. To support abstract reasoning over such systems, we introduce the notion of focus set \u2014 a selected set of logical formul\u00e6 that provide an abstraction from the underlying system state. Based on this abstraction, we define global and distributed symbolic representations of epistemic states, along with representable epistemic actions that enable efficient symbolic updates. For formal analysis, we define a generic operational semantics and develop and relate three complementary semantic frameworks: (1)\u00a0a semantic environment, where system states are modelled as epistemic states, (2)\u00a0a symbolic environment, where knowledge is represented as sets of logical formul\u00e6, and (3)\u00a0a distributed environment, represented by a family of local knowledge bases where each agent has its own local symbolic state. We establish a correspondence between these environments via a notion of relative elementary equivalence. Our main result demonstrates that equivalent configurations simulate each other\u2019s behaviour and satisfy the same dynamic epistemic formul\u00e6, ensuring representational consistency across all three perspectives. This provides a robust foundation for reasoning about distributed knowledge and belief dynamics in cooperative multi-agent systems.<\/jats:p>","DOI":"10.1007\/s10009-026-00855-z","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T13:51:15Z","timestamp":1774360275000},"page":"167-184","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Epistemic ensembles in semantic, symbolic, and distributed environments"],"prefix":"10.1007","volume":"28","author":[{"given":"Alexander","family":"Knapp","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rolf","family":"Hennicker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Wirsing","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,24]]},"reference":[{"key":"855_CR1","volume-title":"Stanford Encyclopedia of Philosophy","author":"A. 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