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

Hannes Strass
2015 Journal of Logic and Computation  
We present a translation from defeasible theory bases to abstract dialectical frameworks, a recent generalisation 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
more » ... rules and cyclic (strict and defeasible) supports amongst 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 paper, 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.
doi:10.1093/logcom/exv004 fatcat:hz23guoslvcx7fy7yfx64unfpi