Choices and their Consequences - Explaining Acceptable Sets in Abstract Argumentation Frameworks

We develop a notion of explanations for acceptance of arguments in an abstract argumentation framework.

To this end we show that extensions returned by Dung's standard semantics can be decomposed into

i) non-deterministic choices made on even cycles of the given argumentation graph and then

ii) deterministic iteration of the so-called characteristic function.

Naturally, the choice made in i) can be viewed as an explanation for the corresponding extension and thus the arguments it contains.

We proceed to propose desirable criteria a reasonable notion of an explanation should satisfy.

We present an exhaustive study of the newly introduced notion w.r.t. these criteria.

Finally some interesting decision problems arise from our analysis and we examine their computational complexity, obtaining some surprising tractability results.