A General QBF-based Formalization of abstract Argumentation Theory

We introduce a unified logical approach, based on signed theories and Quantified Boolean Formulas (QBFs), that can serve as a basis for representing and reasoning with various argumentation-based decision problems. By this, we are able to represent, in a uniform and simple way, a wide range of extension-based semantics for argumentation theory, including complete, grounded, preferred, semistable, stage, ideal and eager semantics. Furthermore, our approach involves only propositional languages and quantifications over propositional variables, making decision problems like skeptical and credulous acceptance of arguments simply a matter of logical entailment and satisfiability, which can be verified by existing QBF-solvers.