A new approach for preference-based argumentation frameworks

Article

Abstract

Dung’s argumentation framework consists of a set of arguments and an attack relation among them. Arguments are evaluated and acceptable sets of them, called extensions, are computed using a given semantics. Each extension represents a coherent position. In the literature, several proposals have extended this framework in order to take into account the strength of arguments. The basic idea is to ignore an attack if the attacked argument is stronger than (or preferred to) its attacker. Semantics are then applied using only the remaining attacks. In this paper, we show that those proposals behave correctly when the attack relation is symmetric. However, when it is asymmetric, conflicting extensions may be computed leading to unintended conclusions. We propose an approach that guarantees conflict-free extensions. This approach presents two novelties: the first one is that it takes into account preferences at the semantics level rather than the attack level. The idea is to extend existing semantics with preferences. In case preferences are not available or do not conflict with the attacks, the extensions of the new semantics coincide with those of the basic ones. The second novelty of our approach is that a semantics is defined as a dominance relation on the powerset of the set of arguments. The extensions (under a semantics) are the maximal elements of the dominance relation. Such an approach makes it possible not only to compute the extensions of a framework but also to compare its non-extensions. We start by proposing three dominance relations that generalize respectively stable, preferred and grounded semantics with preferences. Then, we focus on stable semantics and provide full characterizations of its dominance relations and those of its generalized versions. Complexity results are provided. Finally, we show that an instance of the proposed framework retrieves the preferred sub-theories which were proposed in the context of handling inconsistency in weighted knowledge bases.

Keywords

Argumentation Preferences 

Mathematics Subject Classifications (2010)

68T30 68T37 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.IRIT - CNRSToulouse Cedex 9France

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