Affiliations: School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia. [email protected]
Correspondence:
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Address for correspondence: School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
Abstract: There are a wide variety of formalisms for defeasible reasoning that can be seen as implementing concrete argumentation on defeasible rules. However there has been little work on the relationship between such languages and Dung’s abstract argumentation. In this paper we identify two small fragments of defeasible rule languages on which many concrete defeasible formalisms agree. The two fragments are closely related, as we show. Both arise as ways to express abstract argumentation frameworks in the concrete formalisms. Using these fragments, we establish a close relationship between abstract argumentation under semantics based on complete extensions, and ambiguity blocking logics in the framework of Antoniou et al. These results support a uniform approach to deriving complexity lower bounds for defeasible formalisms, where a lower bound is established for abstract argumentation and can then be extended “for free” to corresponding concrete defeasible formalisms.
