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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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.