On Weak Constrained Argumentation Frameworks

The success and popularity of Dung's abstract Argumentation Framework (AF) is also due to its simplicity and expressiveness. Integrity constraints help to express domain knowledge in a compact and natural way, thus keeping easy the modeling task even for problems that otherwise would be hard to encode within an AF. Constraints can be expressed in the so-called Constrained Argumentation Framework (CAF). Although constraints in CAF allow restricting the set of feasible solutions, they can not be used to find “optimal” solutions to problems defined through CAFs. In this paper we present Weak constrained AFs (WAFs) that enhance CAFs with weak constraints, that express some optimal conditions. We discuss the complexity of WAFs under several well-known argumentation semantics, showing that weak constraints increase the expressive power of AFs and CAFs.