Fast Computing of Dung Semantics in Acyclic Probabilistic Argumentation Frameworks
Résumé
This paper presents fast and exact methods for computing the probability of an argument's acceptance using Dung's semantics in the Constellation paradigm of Abstract Argumentation. For (directed) Singly-Connected Graphs (SCGs), the problem can now be solved in linearithmic time instead of being exponential in the number of attacks, as reported in the literature. Moreover, in the more general case of Directed Acyclic Graphs (DAGs), we provide an algorithm whose time complexity is linearithmic in the product of the out-degree of dependent arguments, i.e., arguments reaching the argument considered for acceptance through multiple paths in the graph. We theoretically show that this complexity is lower than the lower-bound of the (exact) Constellation method, which is also supported by empirical results. We also compare our approach on DAGs with the (approximate) Monte-Carlo method, which is stopped when our approach obtains the exact results. Within this time constraint, Monte-Carlo still outputs significant errors, underlying the fast computation of our approach.
Domaines
Informatique [cs]Origine | Fichiers produits par l'(les) auteur(s) |
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