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.
The Mexican group @cite_12 @cite_1 @cite_17 @cite_2 @cite_3 @cite_4 contributes to research on relations of logic programing and argumentation frameworks, too. Their attention is devoted to characterizations of argumentation semantics' in terms of logic programming semantics'. Also a characterization of CF2 is provided in terms of answer set models or stratified argumentation semantics, which is based on stratified minimal models of logic programs.
@cite_4 @cite_1 @cite_3 @cite_2 @cite_12 @cite_17
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It is well-known, in the area of argumentation theory, that there is a direct relationship between extension-based argumentation semantics and logic programming semantics with negation as failure. One of the main implication of this relationship is that one can explore the implementation of argumentation engines by considering logic programming solvers. Recently, it was proved that the argumentation semantics CF2 can be characterized by the stratified minimal model semantics (MM). The stratified minimal model semantics is also a recently introduced logic programming semantics which is based on a recursive construction and minimal models. In this paper, we introduce a solver based on MINISAT algorithm for inferring the logic programming semantics MM∗. As one of the applications of the MM solver, we will argue that this solver is a suitable tool for computing the argumentation semantics CF2. 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. Extension-based argumentation semantics is a successful approach for performing non-monotonic reasoning based on argumentation theory. An interesting property of some extension-based argumentation semantics is that these semantics can be characterized in terms of logic programming semantics. In this paper, we present novel results in this topic. In particular, we show that one can induce an argumentation semantics (that we call Stratified Argumentation Semantics) based on a logic programming semantics that is based on stratified minimal models. We show that the stratified argumentation semantics overcome some problems of extension-based argumentation semantics based on admissible sets and we show that it coincides with the argumentation semantics CF2. Extension-based argumentation semantics have shown to be a suitable approach for performing practical reasoning. Since extension-based argumentation semantics were formalized in terms of relationships between atomic arguments, it has been shown that extension-based argumentation semantics based on admissible sets such as stable semantics can be characterized in terms of answer sets. In this paper, we present an approach for characterizing SCC-recursive semantics in terms of answer set models. In particular, we will show a characterization of CF2 in terms of answer set models. This result suggests that not only extension-based argumentation semantics based on admissible sets can be characterized in terms of answer sets; but also extension-based argumentation semantics based on Strongly Connected Components can be characterized in terms of answer sets.