Winning by numbers: connecting strong admissibility to optimal play in argumentation

Strongly admissible labelings and min-max numberings offer well-founded explanations in formal argumentation. We establish a precise correspondence between min-max numberings and remoteness functions from combinatorial game theory, showing that min-max numbers characterize optimal play length, i.e., where players seek the fastest win or longest delay of loss. Our game–argumentation duality strengthens the theoretical and computational foundations for cross-fertilization between argumentation and game theory: game-theoretic provenance explanations apply to argumentation frameworks; pure strategy-based provenance aligns with strongly admissible labelings; and a linear-time algorithm for computing remoteness is sufficient to compute grounded labelings and min-max numbers.