Instantiating rule-based defeasible theories in abstract dialectical frameworks and beyond

摘要

We present a translation from defeasible theory bases to abstract dialectical frameworks, a recent generalization of abstract argumentation frameworks. Using several problematic examples from the literature, we first show how our translation addresses important issues of existing approaches. We then prove that the translated frameworks satisfy the rationality postulates closure and direct/indirect consistency. Furthermore, the frameworks can detect inconsistencies in the set of strict inference rules and cyclic (strict and defeasible) supports among literals. We also show that the translation involves at most a quadratic blowup and is, therefore, effectively and efficiently computable. In the last part of the article, we also define a direct, possible-worlds semantics for defeasible theory bases, which illustrates the technical difficulties arising in this process. In particular, the possible-worlds semantics is eager to apply defeasible rules, which is in contrast to the previously studied translation-based approaches.