Relating the Semantics of Abstract Dialectical Frameworks and Standard AFs
Gerhard Brewka, Paul Dunne and Stefan Woltran
One criticism often advanced against abstract argumentation frameworks (AFs), is that these consider only one form of interaction between atomic arguments: specifically that an argument attacks another. Attempts to broaden the class of relationships include bipolar frameworks, where arguments support others, and abstract dialectical frameworks (ADFs). The latter, allow ``acceptance'' of an argument, x, to be predicated on a given propositional function, C_x, dependent on the corresponding acceptance of its parents, i.e. those y for which <y,x> occurs. Although offering a richly expressive formalism subsuming both standard and bipolar AFs, an issue that arises with ADFs is whether this expressiveness is achieved in a manner that would be infeasible within standard AFs, e.g. can the semantics used in ADFs be mapped to some AF semantics? How many arguments are needed in an AF to ``simulate'' an ADF? We show that any ADF can be simulated (in a formally defined sense) by an AF of similar size and that this translation can be realised by a polynomial time algorithm.