On the computation of top-k extensions in abstract argumentation frameworks

Formal argumentation has received a lot of attention during the last two decades, since abstract argumentation framework provides the basis for various reasoning problems in Artificial Intelligence. Unfortunately, the exponential number of its possible semantics extensions makes some reasoning problems intractable in this framework. In this paper, we investigate the pivotal issue of efficient computation of acceptable arguments called extensions according to a given semantics. In particular, we address this aspect by applying a strategy of how to use preferences at the semantics level in order to determine what are "desirable" outcomes of the argumentation process. Then, we present a new approach for computing the Top-κ extensions of an abstract argumentation framework, according to a user-specified preference relation. Indeed, an extension is a Top-κ extension for a given semantics if it admits less than k extensions preferred to it with respect to a preference relation. Our experiments on various datasets demonstrate the effectiveness and scalability of our approach and the accuracy of the proposed enumeration method.