{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,9]],"date-time":"2026-08-09T04:40:52Z","timestamp":1786250452694,"version":"3.56.0"},"reference-count":66,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:00:00Z","timestamp":1556755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011730","name":"Templeton World Charity Foundation","doi-asserted-by":"publisher","award":["TWCF0067\/AB41"],"award-info":[{"award-number":["TWCF0067\/AB41"]}],"id":[{"id":"10.13039\/501100011730","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011730","name":"Templeton World Charity Foundation","doi-asserted-by":"publisher","award":["TWCF0196"],"award-info":[{"award-number":["TWCF0196"]}],"id":[{"id":"10.13039\/501100011730","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Actual causation is concerned with the question: \u201cWhat caused what?\u201d Consider a transition between two states within a system of interacting elements, such as an artificial neural network, or a biological brain circuit. Which combination of synapses caused the neuron to fire? Which image features caused the classifier to misinterpret the picture? Even detailed knowledge of the system\u2019s causal network, its elements, their states, connectivity, and dynamics does not automatically provide a straightforward answer to the \u201cwhat caused what?\u201d question. Counterfactual accounts of actual causation, based on graphical models paired with system interventions, have demonstrated initial success in addressing specific problem cases, in line with intuitive causal judgments. Here, we start from a set of basic requirements for causation (realization, composition, information, integration, and exclusion) and develop a rigorous, quantitative account of actual causation, that is generally applicable to discrete dynamical systems. We present a formal framework to evaluate these causal requirements based on system interventions and partitions, which considers all counterfactuals of a state transition. This framework is used to provide a complete causal account of the transition by identifying and quantifying the strength of all actual causes and effects linking the two consecutive system states. Finally, we examine several exemplary cases and paradoxes of causation and show that they can be illuminated by the proposed framework for quantifying actual causation.<\/jats:p>","DOI":"10.3390\/e21050459","type":"journal-article","created":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T03:15:22Z","timestamp":1556766922000},"page":"459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["What Caused What? A Quantitative Account of Actual Causation Using Dynamical Causal Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1000-9917","authenticated-orcid":false,"given":"Larissa","family":"Albantakis","sequence":"first","affiliation":[{"name":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William","family":"Marshall","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"},{"name":"Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Erik","family":"Hoel","sequence":"additional","affiliation":[{"name":"Allen Discovery Center, Tufts University, Medford, MA 02155, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulio","family":"Tononi","sequence":"additional","affiliation":[{"name":"Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,2]]},"reference":[{"key":"ref_1","unstructured":"Illari, M., Phyllis, F.R., and Williamson, J. 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