Breaking Predictions Is Not Enough: Specified-Foil Counterfactuals for Temporal Graphs

Temporal graph counterfactual explanations typically change past events to change or invalidate an original prediction, while leaving its replacement unspecified. Yet a user facing a predicted outcome often asks which past conditions would make a particular alternative occur instead. We formulate this destination-specific question as the Specified-Foil Counterfactual: given an original prediction A and a foil B fixed before search, find a low-cost past-event intervention under which the same predictor selects B as top-ranked. Our trace-guided intervention search contrasts the completed execution of A with a reconstructed incomplete execution of B, maps their difference to DELETE, INSERT, REWIRE, RELABEL, and SHIFT operations, and verifies B through exact replay. We instantiate this principle with LiFTER on continuous-time dynamic graphs and TLogic on temporal knowledge graphs. On CTDGs, the method retains 85.7-93.6% of black-box greedy successes while reducing predictor evaluations by 75.0-80.0%; on TKGs, it reaches the specified foil in 74.8% of 600 comparisons. Executable traces thereby become computational structures for constructing conditions of unselected alternatives, rather than records used only to explain predictions already made.