Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding an exponential number of terms. We show that this exponential blowup can be avoided in an interesting fragment of epistemic probabilistic argumentation and that some computational problems that have been considered intractable can be solved in polynomial time. We give efficient convex programming formulations for these problems and explore how far our fragment can be extended without loosing tractability.
@cite_36 recently introduced a very general probabilistic argumentation framework that generalizes many ideas that have been considered before in the literature. The authors consider probability functions over subsets of defeasible theories or over subgraphs. The latter approach can then be seen as a generalization of the former, which abstracts from the structure of arguments. The authors discuss probabilistic labellings that should not be confused with probability labellings that we considered here. Roughly speaking, in @cite_36 , a probabilistic labelling frame corresponds to a probability function over subsets of possible classical labellings over an argumentation framework. These probabilistic labelling frames can then be used to assign probabilities to arguments. In this sense, a probabilistic labelling considered in @cite_36 induces a probability labelling as considered here. However, the focus in @cite_36 is on conceptual questions and computational problems are not discussed.
@cite_36
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The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.