There are various interesting semantics' (extensions) designed for argumentation frameworks. They enable to assign a meaning, e.g., to odd-length cycles. Our main motivation is to transfer semantics' proposed by Baroni, Giacomin and Guida for argumetation frameworks with odd-length cycles to logic programs with odd-length cycles through default negation. The developed construction is even stronger. For a given logic program an argumentation framework is defined. The construction enables to transfer each semantics of the resulting argumentation framework to a semantics of the given logic program. Weak points of the construction are discussed and some future continuations of this approach are outlined.
Abstract argumentation frameworks nowadays provide the most popular formalization of argumentation on a conceptual level. Numerous semantics for this paradigm have been proposed, whereby cf2 semantics has shown to nicely solve particular problems concernend with odd-length cycles in such frameworks. In order to compare different semantics not only on a theoretical basis, it is necessary to provide systems which implement them within a uniform platform. Answer-Set Programming (ASP) turned out to be a promising direction for this aim, since it not only allows for a concise representation of concepts inherent to argumentation semantics, but also offers sophisticated off-the-shelves solvers which can be used as core computation engines. In fact, many argumentation semantics have meanwhile been encoded within the ASP paradigm, but not all relevant semantics, among them cf2 semantics, have yet been considered. The contributions of this work are thus twofold. Due to the particular nature of cf2 semantics, we first provide an alternative characterization which, roughly speaking, avoids the recursive computation of sub-frameworks. Then, we provide the concrete ASP-encodings, which are incorporated within the ASPARTIX system, a platform which already implements a wide range of semantics for abstract argumentation. The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dung's argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user. Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity.