For Incomplete Argumentation Frameworks (IAFs), the notion of stability is of importance by indicating whether there is no need anymore to investigate the existence of currently uncertain elements. Further, the notion of relevance characterizes the actions required for the stability to occur in the future. In this study, we point out that the relevance of elements is not an independent matter, and the addition or removal of one relevant element may have impact on other relevant elements by leading them to turn irrelevant automatically. Based on this observation, we propose an impact-based method to resolve uncertainty in IAFs for reaching stability of a given set of arguments under five common semantics. This method iteratively performs the relevant action that has the largest impact until all relevant elements have become irrelevant. We give theoretical foundations of the method and effective ways to compute the impact under various semantics. Specifically, for admissible and stable semantics, we give characterizing conditions for directly identifying the impact of a relevant element, and then show that our impact-based method only has to decide the minimum number of uncertain elements in order to reach stability of the given set necessarily being an extension.

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Recognizing the Impact Among Relevant Elements for Reaching Stability in Incomplete Argumentation Frameworks

  • Anshu Xiong,
  • Songmao Zhang

摘要

For Incomplete Argumentation Frameworks (IAFs), the notion of stability is of importance by indicating whether there is no need anymore to investigate the existence of currently uncertain elements. Further, the notion of relevance characterizes the actions required for the stability to occur in the future. In this study, we point out that the relevance of elements is not an independent matter, and the addition or removal of one relevant element may have impact on other relevant elements by leading them to turn irrelevant automatically. Based on this observation, we propose an impact-based method to resolve uncertainty in IAFs for reaching stability of a given set of arguments under five common semantics. This method iteratively performs the relevant action that has the largest impact until all relevant elements have become irrelevant. We give theoretical foundations of the method and effective ways to compute the impact under various semantics. Specifically, for admissible and stable semantics, we give characterizing conditions for directly identifying the impact of a relevant element, and then show that our impact-based method only has to decide the minimum number of uncertain elements in order to reach stability of the given set necessarily being an extension.