The Skeptic’s Argumentation Game or: Well-Founded Explanations for Mere Mortals

We propose a new discussion game for abstract argumentation frameworks (AFs), related to, but different from other dialectical proof procedures and discussion games: the Skeptic’s Argumentation Game (SAG). Unlike in other AF games, Player I (the Skeptic) aims to establish that an argument x is defeated, while Player II (the Optimist) tries to prove the opponent wrong, i.e., that x is accepted. If neither player has a winning strategy, the position is a draw and x’s status is undecided. This “reversal of roles” (compared to the usual Proponent vs Opponent dialogue games about the acceptance status of an argument) might appear strange at first, but has a number of important, fruitful consequences. Since SAG corresponds exactly to (i) the grounded labeling semantics of AFs, and (ii) the standard semantics of “win-move” (WM) games for normal play on finite graphs, a rich body of research and results can be transferred directly to grounded AF labelings. In this paper we show one such result transfer: The value (WON/LOST/DRAWN) of a position x in a solved WM game can be fully explained by the provenance of x, i.e., a subgraph definable by a regular expression. Consequently, via SAG, we can provide a detailed, well-founded explanation for the acceptance status (value) of an argument. We also exploit well-founded explanations for visualization to expose the structural dependencies inherent in an AF under the grounded semantics.