Abstract
Combining computational models of argumentation with probability theory has recently gained increasing attention, in particular with respect to abstract argumentation frameworks. Approaches following this idea can be categorised into the constellations and the epistemic approach. While the former considers probability functions on the subgraphs of abstract argumentation frameworks, the latter uses probability theory to represent degrees of belief in arguments, given a fixed framework. In this paper, we investigate the case where probability functions are given on the extensions of abstract argumentation frameworks. This generalises classical semantics in a straightforward fashion and we show that our approach also complies with many postulates for epistemic probabilistic argumentation.
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Notes
- 1.
Note that the definitional relation for \(P^{\subseteq }(E)\) in (1) does not carry over to \(\underline{P}^{\subseteq }(E)\), i.e. in general it does not hold that \(\underline{P}^{\subseteq }(E) = \sum _{E' \in 2^{\mathsf {Arg}} , E \subseteq E'}\underline{P}(E')\). An analogous consideration applies to \(\underline{P}^{\in }(\mathcal {A})\).
- 2.
In fact, on finite algebras of events the notions of dF-coherent probabilities, finitely additive probabilities and \(\sigma \)-additive probabilities coincide.
- 3.
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The authors are grateful to the anonymous referees for their helpful comments.
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Thimm, M., Baroni, P., Giacomin, M., Vicig, P. (2018). Probabilities on Extensions in Abstract Argumentation. In: Black, E., Modgil, S., Oren, N. (eds) Theory and Applications of Formal Argumentation. TAFA 2017. Lecture Notes in Computer Science(), vol 10757. Springer, Cham. https://doi.org/10.1007/978-3-319-75553-3_7
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