AGM Meets Abstract Argumentation: Expansion and Revision for Dung Frameworks

Abstract

In this paper we combine two of the most important areas of knowledge representation, namely belief revision and (abstract) argumentation. More precisely, we show how AGM-style expansion and revision operators can be defined for Dung's abstract argumentation frameworks (AFs). Our approach is based on a reformulation of the original AGM postulates for revision in terms of monotonic consequence relations for AFs. The latter are defined via a new family of logics, called Dung logics, which satisfy the important property that ordinary equivalence in these logics coincides with strong equivalence for the respective argumentation semantics. Based on these logics we define expansion as usual via intersection of models. We show the existence of such operators. This is far from trivial and requires to study realizability in the context of Dung logics. We then study revision operators. We show why standard approaches based on a distance measure on models do not work for AFs and present an operator satisfying all postulates for a specific Dung logic.