Argumentation frameworks, games and kernels: time for a family reunion!

Formal argumentation, logic programming, game theory and database theory have evolved independently, despite sharing deep foundational links. We show how a single, unstratified logic rule appears in several equivalent forms, including as Dung’s argumentation processing unit and a meta-interpreter for solving win-move games, thereby providing a shared foundation that can be used to reconnect the concepts and techniques from the different communities. We formalize dualities and connections between abstract argumentation frameworks (AFs), cooperative and combinatorial games and digraph kernels. Through these connections we discover a new, canonical discussion game: the Skeptic’s Argumentation Game is the most immediate two-player game for the grounded AF semantics. Classic results transfer seamlessly as well: Smith’s remoteness function provides a linear-time method for computing the grounded labelling and the associated min-max numberings of strongly admissible labellings on finite AF graphs. Fraenkel’s kernel decomposition theorem applies to AFs, and provenance concepts from database theory yield fine-grained explanations for argument acceptance. By making these various historic and new correspondences explicit, we invite the community to join our ‘family reunion’, enabling the transfer of concepts, algorithms and insights between formal argumentation, game theory and graph theory, thereby opening new opportunities and deepening the theoretical foundations of all three.