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The concept of ambiguous literals of defeasible logics is mapped to the set of undecided arguments identified by an argumentation semantics. It follows that Dung’s complete semantics are all ambiguity propagating, since the undecided status of an attacking argument is always propagated to the attacked argument, unless the latter is defeated by another accepted argument. In this paper we investigate a novel family of abstract argumentation semantics, called weakly-admissible semantics, where we do not require an acceptable argument to be necessarily defended from the attacks of undecided arguments. Weakly-admissible semantics are conflict-free, ambiguity blocking, non-admissible (in Dung’s sense), but employing a more relaxed defence-based notion of admissibility; they allow reinstatement and generate extensions that are super-sets of grounded semantics, and they at least accept credulously what Dung’s complete semantics accept at least credulously.
Dondio, P. (2019) Weakly-admissible Semantics and the Propagation of Ambiguity in Abstract Argumentation Semantics, Technological Report.