Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSX @math . Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.
In @cite_20 , an argumentation semantics for extended logic programs, similar to Prakken and Sartor's, is proposed; it is influenced by WFSX, and distinguishes between sceptical and credulous conclusions of an argument. It also provides a proof theory based on dialogue trees, similar to Prakken and Sartor's.
@cite_20
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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. We propose a new graded semantics for abstract argumentation frameworks that is based on the constellations approach to probabilistic argumentation. Given an abstract argumentation framework, our approach assigns uniform probability to all arguments and then ranks arguments according to the probability of acceptance wrt. some classical semantics. Albeit relying on a simple idea this approach (1) is based on the solid theoretical foundations of probability theory, and (2) complies with many rationality postulates proposed for graded semantics. We also investigate an application of our approach for inconsistency measurement in argumentation frameworks and show that the measure induced by the probabilistic graded semantics also complies with the basic rationality postulates from that area. The ability to view extended logic programs as argumentation systems opens the way for the use of this language in formalizing communication among reasoning computing agents in a distributed framework. In this paper we define an argumentative and cooperative multi-agent framework, introducing credulous and sceptical conclusions. We also present an algorithm for inference and show how the agents can have more credulous or sceptical conclusions.