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.
Relations between the classic'' argumentation semantics' and corresponding semantic views on logic programs is studied in @cite_6 . Of course, the problem of odd cycles is not tackled in the paper. Our future goal is a detailed comparison of constructions of @cite_6 and ours.
@cite_6
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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. Classical semantics for abstract argumentation frameworks are usually defined in terms of extensions or, more recently, labelings. That is, an argument is either regarded as accepted with respect to a labeling or not. In order to reason with a specific semantics one takes either a credulous or skeptical approach, i. e. an argument is ultimately accepted, if it is accepted in one or all labelings, respectively. In this paper, we propose a more general approach for a semantics that allows for a more fine-grained differentiation between those two extreme views on reasoning. In particular, we propose a probabilistic semantics for abstract argumentation that assigns probabilities or degrees of belief to individual arguments. We show that our semantics generalizes the classical notions of semantics and we point out interesting relationships between concepts from argumentation and probabilistic reasoning. We illustrate the usefulness of our semantics on an example from the medical domain. 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 paper tackled the issue of arguments evaluation in weighted bipolar argumentation graphs (i.e., graphs whose arguments have basic strengths, and may be both supported and attacked). We introduce axioms that an evaluation method (or semantics) could satisfy. Such axioms are very useful for judging and comparing semantics. We then analyze existing semantics on the basis of our axioms, and finally propose a new semantics for the class of acyclic graphs.