On Preferences and Priority Rules in Abstract Argumentation

Dung’s abstract Argumentation Framework (AF) has emerged as a central formalism for argumentation in AI. Preferences in AF allow to represent the comparative strength of arguments in a simple yet expressive way. In this paper we first investigate the complexity of the verification as well as credulous and skeptical acceptance problems in Preferencebased AF (PAF) that extends AF with preferences over arguments. Next, after introducing new semantics for AF where extensions are selected using cardinality (instead of set inclusion) criteria and investigating their complexity, we introduce a framework called AF with Priority rules (AFP) that extends AF with sequences of priority rules. AFP generalizes AF with classical set-inclusion and cardinality based semantics, suggesting that argumentation semantics can be viewed as ways to express priorities among extensions. Finally, we extend AFP by proposing AF with Priority rules and Preferences (AFP^2), where also preferences over arguments can be used to define priority rules, and study the complexity of the above-mentioned problems.