The Degrees of Monotony-Dilemma in Abstract Argumentation

In this paper, we introduce the notion of the degree of monotony to abstract argumentation, a well-established method for drawing inferences in face of conflicts in non-monotonic reasoning. Roughly speaking, the degree of monotony allows us, given an abstract argumentation semantics and an abstract argumentation framework to be as monotonic as possible, when iteratively drawing inferences and expanding the argumentation framework. However, we also show that when expanding an argumentation framework several times using so-called normal expansions, an agent may, at any given step, select a conclusion that has the highest degree of monotony w.r.t. the previous conclusion (considering the constraints of the semantics), but end up with a conclusion that has a suboptimal degree of monotony w.r.t. one or several conclusions that precede the previous conclusion. We formalize this observation as the degrees of monotony-dilemma.