Minimal hypotheses: extension-based semantics to argumentation

  • Authors:

  • Zhihu Zhang;Zuoquan Lin

  • Affiliations:

  • Nanjing Institute of Electronic Technology, Nanjing, China 210039 and Department of Information Science, School of Mathematical Sciences, Peking University, Beijing, China 100871;Department of Information Science, School of Mathematical Sciences, Peking University, Beijing, China 100871

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2012

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Abstract

The emptiness problem of the preferred semantics and the non-existence problem of the stable semantics are well recognized for argumentation frameworks. In this paper, we introduce two strong semantics, named s-preferred semantics and s-stable semantics, to guarantee the non-emptiness of the preferred extensions and the existence of the stable extensions respectively. Our semantics are defined by two concepts of extensions of argumentation frameworks, namely s-preferred extension and s-stable extension. Each is constructed in a similar way to the original semantics. The novelty of our semantics is that an extension of an argumentation framework is considered as a pair of sets of arguments, in which the second element of an extension is viewed as a kind of hypotheses that should be minimized. The s-preferred semantics not only solves the emptiness problem of the preferred semantics, but also coincides with the preferred semantics when nonempty preferred extensions exist. Meanwhile, the s-stable semantics ensures the existence of extensions, and coincides with the stable semantics when the stable extensions exist as well. The relations among various semantics for argumentation frameworks are discussed.