Tracing Actual Causes with Counterfactual Witness Maps

Halpernian actual causation, the formal study of which events in a specific situation caused a specific outcome in acyclic structural causal models, underpins legal responsibility, moral blame, and the assessment of causal harm. Despite the rich logical framework, no prior sound and complete enumeration procedure is known for finding all actual causes in a given setting, blocking downstream tasks such as responsibility attribution, blame assessment, and causal-harm grading that aggregate over the full cause set. We close this gap by introducing witness targets: sets of joint configurations containing every counterfactual witness. In combination with an ancestor intervention grammar we derive a finite directed acyclic witness map. We prove that for every actual cause there exists a contingency set such that the joint intervention set appears as a node of this map, and present an algorithm for Tracing Actual Causes (TrAC) that is sound and complete for enumerating all actual causes of any target event. We compare TrAC empirically with existing single-cause baselines on random Boolean structural causal models, demonstrating practical feasibility for graphs of up to 15 nodes.