A Logical Encoding for k-m-Realization of Extensions in Abstract Argumentation
Résumé
We study the notion of realization of extensions in abstract argumentation. It consists in reversing the usual reasoning process: instead of computing the extensions of an argumentation framework, we want to determine whether a given set of extensions corresponds to some (set of) argumentation framework(s) (AFs); and more importantly we want to identify such an AF (or set of AFs) that realizes the set of extensions. While deep theoretical studies have been concerned with realizability of extensions sets, there are few computational approaches for solving this problem. In this paper, we generalize the concept of realizability by introducing two parameters: the number k of auxiliary arguments (i.e. those that do not appear in any extension), and the number m of AFs in the result. We define a translation of k-m-realizability into Quantified Boolean Formulas (QBFs) solving. We also show that our method allows to guarantee that the result of the realization is as close as possible to some input AF. Our method can be applied in the context of AF revision operators, where revised extensions must be mapped to a set of AFs while ensuring some notion of proximity with the initial AF.
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