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Abstract
Abstract dialectical frameworks (ADFs) constitute a recent and powerful generalisation of Dung's argumentation frameworks (AFs), where the relationship between the arguments can be 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 give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. We refer to the appendix for rewritings of all encodings (of non-trivial reasoning tasks) in such a manner that their structure reflects the complexity of the associated reasoning problems, that is, the encodings are transformed to PNF or, when they correspond to complete problems, are written in such a way that they mirror the structure of the SAT UNSAT problem.