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.
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. Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t. AF. In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics. Extension-based argumentation semantics have been 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 (such as the grounded semantics and stable semantics) can be characterized by logic programming semantics with negation as failure. Recently, it has been shown that argumentation semantics such as the preferred semantics and the CF2 semantics can be characterized in terms of logic programming semantics. In this paper, we make a short overview w.r.t. recent results in the close relationship between extension-based semantics and logic programming semantics with negation as failure. We also show that there is enough evidence to believe that the use of declarative approaches based on logic programming semantics with negation as failure is a practical approach for performing practical reasoning following an argumentation reasoning approach. 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. A polyamide resin composition comprises melamine cyanurate with or without a copper compound, an alkali met al halide, a tin compound, a bisamide compound or a bisureido compound. 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.