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We study rankings over labelings as a generalization of traditional labeling-based semantics in abstract argumentation. Our approach is an alternative to recent developments on rankings over arguments. The formal basis is a qualitative abstraction of probability theory called ranking theory. We propose a fundamental property, called SCC stratification, that a ranking-theoretic semantics can be expected to satisfy, present a general scheme to define a ranking-theoretic semantics, and determine conditions under which this scheme satisfies SCC stratification.
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