Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted to new beliefs using update operators. While the use of probability functions puts this approach on a solid foundational basis, it also causes computational challenges as the amount of data to process depends exponentially on the number of arguments. This leads to bottlenecks in applications such as modelling opponent's beliefs for persuasion dialogues. We show how update operators over probability functions can be related to update operators over much more compact representations that allow polynomial-time updates. We discuss the cognitive and probabilistic-logical plausibility of this approach and demonstrate its applicability in computational persuasion.
One limitation when restricting to probability labellings is that we cannot compute the probabilities of complex formulas over arguments anymore without adding further assumptions. However, as we demonstrated, we can sometimes do without complex formulas. In this context, probability labellings can be seen as an alternative to weighted argumentation frameworks that also assign a strength value between @math and @math to arguments @cite_1 @cite_2 @cite_26 @cite_19 @cite_35 . What makes probability labellings an interesting alternative is their well-defined relationship to probability functions and probability theory.
@cite_35 @cite_26 @cite_1 @cite_19 @cite_2
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Agents engage in dialogues having as goals to make some arguments acceptable or unacceptable. To do so they may put forward arguments, adding them to the argumentation framework. Argumentation semantics can relate a change in the framework to the resulting extensions but it is not clear, given an argumentation framework and a desired acceptance state for a given set of arguments, which further arguments should be added in order to achieve those justification statuses. Our methodology, called conditional labelling, is based on argument labelling and assigns to each argument three propositional formulae. These formulae describe which arguments should be attacked by the agent in order to get a particular argument in, out, or undecided, respectively. Given a conditional labelling, the agents have a full knowledge about the consequences of the attacks they may raise on the acceptability of each argument without having to recompute the overall labelling of the framework for each possible set of attack they may raise. We provide a model for reasoning about knowledge and probability together. We allow explicit mention of probabilities in formulas, so that our language has formulas that essentially say «according to agent i, formula φ holds with probability at least b.» The language is powerful enough to allow reasoning about higher-order probabilities, as well as allowing explicit comparisons of the probabilities an agent places on distinct events. We present a general framework for interpreting such formulas, and consider various properties that might hold of the interrelationship between agents' probability assignments at different states. We provide a complete axiomatization for reasoning about knowledge and probability, prove a small model property, and obtain decision procedures The choice of the loss function is critical in extreme multi-label learning where the objective is to annotate each data point with the most relevant subset of labels from an extremely large label set. Unfortunately, existing loss functions, such as the Hamming loss, are unsuitable for learning, model selection, hyperparameter tuning and performance evaluation. This paper addresses the issue by developing propensity scored losses which: (a) prioritize predicting the few relevant labels over the large number of irrelevant ones; (b) do not erroneously treat missing labels as irrelevant but instead provide unbiased estimates of the true loss function even when ground truth labels go missing under arbitrary probabilistic label noise models; and (c) promote the accurate prediction of infrequently occurring, hard to predict, but rewarding tail labels. Another contribution is the development of algorithms which efficiently scale to extremely large datasets with up to 9 million labels, 70 million points and 2 million dimensions and which give significant improvements over the state-of-the-art. This paper's results also apply to tagging, recommendation and ranking which are the motivating applications for extreme multi-label learning. They generalize previous attempts at deriving unbiased losses under the restrictive assumption that labels go missing uniformly at random from the ground truth. Furthermore, they provide a sound theoretical justification for popular label weighting heuristics used to recommend rare items. Finally, they demonstrate that the proposed contributions align with real world applications by achieving superior clickthrough rates on sponsored search advertising in Bing. 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.