{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T07:00:04Z","timestamp":1762326004539,"version":"build-2065373602"},"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":[[2025,11]]},"abstract":"<jats:p>Graph Neural Networks (GNNs) are a class of machine-learning models that operate on graph-structured data.  Their expressive power is intimately related to logics that are invariant under graded bisimilarity. Current proposals for recurrent GNNs either assume that the graph size is given to the model, or suffer from a lack of termination guarantees.  In this paper, we propose a halting mechanism for recurrent GNNs.  We prove that our halting model can express all node classifiers definable in graded modal mu-calculus, even for the standard GNN variant that is oblivious to the graph size.  To prove our main result, we develop a new approximate semantics for graded mu-calculus, which we believe to be of independent interest.  We leverage this new semantics into a new model-checking algorithm, called the counting algorithm, which is oblivious to the graph size. In a final step we show that the counting algorithm can be implemented on a halting recurrent GNN.<\/jats:p>","DOI":"10.24963\/kr.2025\/18","type":"proceedings-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:10:44Z","timestamp":1762323044000},"page":"175-184","source":"Crossref","is-referenced-by-count":0,"title":["Halting Recurrent GNNs and the Graded mu-Calculus"],"prefix":"10.24963","author":[{"given":"Jeroen","family":"Bollen","sequence":"first","affiliation":[{"name":"Data Science Institute, Hasselt University, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Van den Bussche","sequence":"additional","affiliation":[{"name":"Data Science Institute, Hasselt University, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stijn","family":"Vansummeren","sequence":"additional","affiliation":[{"name":"Data Science Institute, Hasselt University, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonni","family":"Virtema","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Sheffield, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10584","event":{"name":"22nd International Conference on Principles of Knowledge Representation and Reasoning {KR-2025}","theme":"Artificial Intelligence","location":"Melbourne, Australia","acronym":"KR-2025","number":"22","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","Academic College of Tel-Aviv","European Association for Artificial Intelligence","National Science Foundation"],"start":{"date-parts":[[2025,11,11]]},"end":{"date-parts":[[2025,11,17]]}},"container-title":["Proceedings of the TwentySecond International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:10:58Z","timestamp":1762323058000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2025\/18"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2025,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2025\/18","relation":{},"subject":[],"published":{"date-parts":[[2025,11]]}}}