In this paper, we tackle the problem of efficiently recomputing the skeptical acceptance of dynamic argumentation frameworks under the well-known preferred semantics. We discuss an incremental algorithmic solution whose main idea is that of exploiting the initial knowledge (including the update to perform) in order to identify a potentially small portion of the argumentation framework. Such a portion is sufficient to compute the skeptical preferred acceptance of a goal argument w.r.t. the whole updated framework. We also discuss on how similar ideas extend to more general argumentation frameworks.
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