Games and Argumentation: Time for a Family Reunion!

Abstract

The rule "defeated(X) $\leftarrow$ attacks(Y,X), $\neg$ defeated(Y)" states that an argument is defeated if it is attacked by an argument that is not defeated. The rule "win(X) $\leftarrow$ move(X,Y), $\neg$ win(Y)" states that in a game a position is won if there is a move to a position that is not won. Both logic rules can be seen as close relatives (even identical twins) and both rules have been at the center of attention at various times in different communities: The first rule lies at the core of argumentation frameworks and has spawned a large family of models and semantics of abstract argumentation. The second rule has played a key role in the quest to find the "right" semantics for logic programs with recursion through negation, and has given rise to the stable and well-founded semantics. Both semantics have been widely studied by the logic programming and nonmonotonic reasoning community. The second rule has also received much attention by the database and finite model theory community, e.g., when studying the expressive power of query languages and fixpoint logics. Although close connections between argumentation frameworks, logic programming, and dialogue games have been known for a long time, the overlap and cross-fertilization between the communities appears to be smaller than one might expect. To this end, we recall some of the key results from database theory in which the win-move query has played a central role, e.g., on normal forms and expressive power of query languages. We introduce some notions that naturally emerge from games and that may provide new perspectives and research opportunities for argumentation frameworks. We discuss how solved query evaluation games reveal how- and why-not provenance of query answers. These techniques can be used to explain how results were derived via the given query, game, or argumentation framework.