{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T12:04:22Z","timestamp":1784203462052,"version":"3.55.0"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:p>This paper establishes and proves representation theorems for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. Cumulative logics are famously given by System~C. For propositional dependence logic, we show that System C entailments are exactly captured by cumulative models from Kraus, Lehmann and Magidor. On the other hand, we show that entailment in cumulative propositional logics with team semantics is exactly captured by cumulative and asymmetric models. For the latter, we also obtain equivalence with cumulative logics based on propositional logic with classical semantics. The proofs will be useful for proving representation theorems for other cumulative logics without negation and material implication.<\/jats:p>","DOI":"10.24963\/kr.2026\/40","type":"proceedings-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T11:15:53Z","timestamp":1784200553000},"page":"423-428","source":"Crossref","is-referenced-by-count":0,"title":["Representation Theorems for Cumulative Propositional Dependence Logics"],"prefix":"10.24963","author":[{"given":"Juha","family":"Kontinen","sequence":"first","affiliation":[{"name":"University of Helsinki"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arne","family":"Meier","sequence":"additional","affiliation":[{"name":"Leibniz University Hannover"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Sauerwald","sequence":"additional","affiliation":[{"name":"University of Hagen"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"10584","event":{"name":"23nd International Conference on Principles of Knowledge Representation and Reasoning {KR-2026}","theme":"Artificial Intelligence","location":"Lisbon, Portuagal","acronym":"KR-2026","number":"23","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","European Association for Artificial Intelligence"],"start":{"date-parts":[[2026,7,20]]},"end":{"date-parts":[[2026,7,18]]}},"container-title":["Proceedings of the TwentyThird International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T11:16:05Z","timestamp":1784200565000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2026\/40"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2026\/40","relation":{},"subject":[],"published":{"date-parts":[[2026,7]]}}}