Choices and their Provenance: Explaining Stable Solutions of Abstract Argumentation Frameworks

The rule Defeated() Attacks(, ), Defeated(), evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF): An argument is defeated (out) if there exists an undefeated argument that attacks it.For 2-valued (stable) solutions, this is the case iff is accepted (in), i.e., if all of 's attackers are defeated.Under WFS, arguments that are neither accepted nor defeated are undecided (undec).As shown in prior work, well-founded solutions (a.k.a.grounded labelings) "explain themselves": The provenance of arguments is given by subgraphs (definable via regular path queries) rooted at the node of interest.This provenance is closely related to winning strategies of a two-player argumentation game.We present a novel approach for extending this provenance to stable AF solutions.Unlike grounded solutions, which can be constructed via a bottom-up alternating fixpoint procedure, stable models often involve (non-deterministic) choice as part of the search for models.Thus, the provenance of stable solutions is of a different nature, and reflects a more expressive generate & test paradigm.Our approach identifies minimal sets of critical attacks, pinpointing choices and assumptions made by a stable model.These critical attack edges provide additional insights into the provenance of an argument's status, combining well-founded derivation steps with choice steps.Our approach can be understood as a form of diagnosis that finds minimal "repairs" to an AF graph such that the well-founded solution of the repaired graph coincides with the desired stable model of the original AF graph.