Optimal Correction Sets for Provable Redress of Contestable Causal Discovery

Constraint-based causal discovery relies on conditional-independence (CI) tests that may conflict in finite samples, leaving no causal graph that satisfies them all. Causal Assumption-based Argumentation (ABA) makes these tests explicit as defeasible commitments, and offers correspondence guarantees with a subset of them, but its existing repair procedure releases facts heuristically and offers no formal response to a user's contestation of a release. We argue that contestable causal discovery requires an inspectable repair object, a justification for it, and a predictable revision procedure for such contestations. We therefore formulate CI-fact repair as a minimum-cost correction problem and implement it in Answer Set Programming (ASP). Building on Causal ABA, we provide a compact and efficient ASP encoding of causal consistency, with soundness and completeness guarantees, and a two-way projection correspondence between optimal stable models and minimum-cost correction sets. These results establish fidelity to retained facts, subset-minimality and cost optimality of the repair, conflict-based justifications for released facts, and formally guaranteed redress under user contestations. An empirical evaluation supports the formal account: OptABA-PC retains more correct CI statements, reduces ambiguity in the compatible output causal graphs, while keeping competitive reconstruction performance on common benchmarks with limited number of nodes.