In the context of Dung's abstract framework for argumentation, two main semantics have been considered to assign a defeat status to arguments: the grounded semantics and the preferred semantics. While the two semantics agree in most situations, there are cases where the preferred semantics appears to be more powerful. However, we notice that the preferred semantics gives rise to counterintuitive results in some other cases, related to the presence of odd-length cycles in the attack relation between arguments. To solve these problems, we propose a new semantics which preserves the desirable properties of the preferred semantics, while correctly dealing with odd-length cycles. We check the behavior of the proposed semantics in a number of examples and discuss its relationships with both grounded and preferred semantics.
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