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The traditional 3-valued semantics of an argumentation framework identifies arguments that are “in”, “out” and “undecided”. Yet, it has long been recognised by the community that some elements can be at different degrees in each of these categories [1,2,3]. For example, Dung's semantics can only classify some elements as “out”, but cannot reflect how much “out” they really are or if elements are “in” are they as much “in” as elements which are not attacked at all? In this paper we shall use a numerical approach to give a measure of “in”, “out” and “undecided” to the nodes of a network. We shall devise equations which allow for solutions that reflect these distinctions.
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