Abstract
The existing approaches to formulate the semantics of probabilistic argumentation are based on the notion of possible world. Given a probabilistic argument graph with n nodes, 2 n subgraphs are constructed and their extensions under a given semantics are computed. Then, the probability of a set of arguments E being an extension is equal to the sum of the probabilities of all subgraphs each of which has the extension E. Since in many cases, computing the extensions of a subgraph is computationally expensive, these approaches are fundamentally inefficient or infeasible. In order to cope with this problem, the present paper proposes a novel approach to formulate the semantics of probabilistic argumentation by charactering subgraphs w.r.t. an extension. The results show that under some semantics (admissible, complete, stable), the probability of a set of arguments E being an extension can be obtained without computing the extensions of subgraphs, while under some other semantics (preferred, grounded), only partial computation of extensions is needed.
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