Admissibility in Probabilistic Argumentation

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argumentation is a prominent reasoning framework. It comes with a variety of semantics and has lately been enhanced by probabilities to enable a quantitative treatment of argumentation. While admissibility is a fundamental notion for classical reasoning in abstract argumentation frameworks, it has barely been reflected so far in the probabilistic setting. In this paper, we address the quantitative treatment of abstract argumentation based on probabilistic notions of admissibility. Our approach follows the natural idea of defining probabilistic semantics for abstract argumentation by systematically imposing constraints on the joint probability distribution on the sets of arguments, rather than on probabilities of single arguments. As a result, there might be either a uniquely defined distribution satisfying the constraints, but also none, many, or even an infinite number of satisfying distributions are possible. We provide probabilistic semantics corresponding to the classical complete and stable semantics and show how labeling schemes provide a bridge from distributions back to argument labelings. In relation to existing work on probabilistic argumentation, we present a taxonomy of semantic notions. Enabled by the constraint-based approach, standard reasoning problems for probabilistic semantics can be tackled by SMT solvers, as we demonstrate by a proof-of-concept implementation.


Original languageEnglish
Pages (from-to)957-1009
Number of pages53
JournalJournal of Artificial Intelligence Research
Publication statusPublished - 26 Jun 2022

External IDs

dblp journals/jair/KaferBDDGH22
Scopus 85136562867
Mendeley 94d34c21-9e20-3d80-88be-cced53184a4b
unpaywall 10.1613/jair.1.13530
ORCID /0000-0002-5321-9343/work/142236698
ORCID /0000-0002-0645-1078/work/142250963



  • probabilistic reasoning uncertainty

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