Limits and Possibilities of Forgetting in Abstract Argumentation.

The topic of forgetting has been extensively studied in the field of knowledge representation and reasoning for many major formalisms. Quite recently it has been introduced to abstract argumentation. However, many already known as well as essential aspects about forgetting like strong persistence or strong invariance have been left unconsidered. We show that forgetting in abstract argumentation cannot be reduced to forgetting in logic programming. In addition, we deal with the more general problem of forgetting whole sets of arguments and show that iterative application of existing operators for single arguments does not necessarily yield a desirable result as it may not produce an informationally economic argumentation framework. As a consequence we provide a systematic and exhaustive study of forgetting desiderata and associated operations adapted to the intrinsics of abstract argumentation. We show the limits and shed light on the possibilities.