Preferences and constraints in abstract argumentation

In recent years there has been an increasing interest in extending Dung's framework to facilitate the knowledge representation and reasoning process. In this paper, we present an extension of Abstract Argumentation Framework (AF) that allows for the representation of preferences over arguments' truth values (3-valued preferences). For instance, we can express a preference stating that extensions where argument a is false (i.e. defeated) are preferred to extensions where argument b is false. Interestingly, such a framework generalizes the well-known Preference-based AF with no additional cost in terms of computational complexity for most of the classical argumentation semantics. Then, we further extend AF by considering both (3- valued) preferences and 3-valued constraints, that is constraints of the form φ ⇒ v or v ⇒ φ, where φ is a logical formula and v is a 3-valued truth value. After investigating the complexity of the resulting framework, as both constraints and preferences may represent subjective knowledge of agents, we extend our framework by considering multiple agents and study the complexity of deciding acceptance of arguments in this context.