Reasoning in Abstract Dialectical Frameworks Using Quantified Boolean Formulas

The Abstract dialectical frameworks (ADFs) constitute a recent and powerful generalization of Dung's argumentation frameworks (AFs), where the relationship between the arguments is specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas (QBFs) thus are suitable engines to be employed. In this paper we present QBF encodings on ADF problems generalizing recent work on QBFs for AF labellings. Our encodings not only provide a uniform and modular way of translating reasoning in ADFs to QBFs, but also build the basis for a novel system. We present a prototype implementation for the admissible and preferred semantics and evaluate its performance in comparison with another state-of-the-art tool for ADFs.