On probabilistic argumentation and subargument-completeness

Probabilistic argumentation combines probability theory and formal models of argumentation. Given an argumentation graph where vertices are arguments and edges are attacks or supports between arguments, the approach of probabilistic labellings relies on a probability space where the sample space is any specific set of argument labellings of the graph, so that any labelling outcome can be associated with a probability value. Argument labellings can feature a label indicating that an argument is not expressed, and in previous work these labellings were constructed by exploiting the subargument-completeness postulate according to which if an argument is expressed then its subarguments are expressed and through the use of the concept of ‘subargument-complete subgraphs’. While the use of such subgraphs is interesting to compare probabilistic labellings with other works in the literature, it may also hinder the comprehension of a relatively simple framework. In this short communication, we revisit the construction of probabilistic labellings and demonstrate how labellings can be specified without reference to the concept of subargument-complete subgraphs. By doing so, the framework is simplified and yields a more natural model of argumentation.

Admissibility in Probabilistic Argumentation

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 in the classical setting, it has been merely reflected so far in the probabilistic setting. In this paper, we address the quantitative treatment of argumentation based on probabilistic notions of admissibility in a way that they form fully conservative extensions of classical notions. In particular, our building blocks are not the beliefs regarding single arguments. Instead we start from the fairly natural idea that whatever argumentation semantics is to be considered, semantics systematically induces constraints on the joint probability distribution on the sets of arguments. In some cases there might be many such distributions, even infinitely many ones, in other cases there may be one or none. Standard semantic notions are shown to induce such sets of constraints, and so do their probabilistic extensions. This allows them to be tackled by SMT solvers, as we demonstrate by a proof-of-concept implementation. We present a taxonomy of semantic notions, also in relation to published work, together with a running example illustrating our achievements.

Explainable Acceptance in Probabilistic Abstract Argumentation: Complexity and Approximation

Recently there has been an increasing interest in probabilistic abstract argumentation, an extension of Dung's abstract argumentation framework with probability theory. In this setting, we address the problem of computing the probability that a given argument is accepted. This is carried out by introducing the concept of probabilistic explanation for a given (probabilistic) extension. We show that the complexity of the problem is FP^#P-hard and propose polynomial approximation algorithms with bounded additive error for probabilistic argumentation frameworks where odd-length cycles are forbidden. This is quite surprising since, as we show, such kind of approximation algorithm does not exist for the related FP^#P-hard problem of computing the probability of the credulous acceptance of an argument, even for the special class of argumentation frameworks considered in the paper.

Reasoning with Inconsistent Knowledge using the Epistemic Approach to Probabilistic Argumentation

Structured argumentation involves drawing inferences from knowledge in order to construct arguments and counterarguments. Since knowledge can be uncertain, we can use a probabilistic approach to representing and reasoning with the knowledge. Individual arguments can be constructed from the knowledge, with the belief in each argument determined just from the belief in the formulae appearing in the argument. However, if the original knowledgebase is inconsistent, this does not take into account the counterarguments that can be constructed. We therefore need a wider perspective that revises the belief in individual arguments in order to take into account the counterarguments. To address this need, we present a framework for probabilistic argumentation that uses relaxation methods to give a coherent view on the knowledge, and thereby revises the belief in the arguments that are generated from the knowledge.

Neuro-Symbolic Probabilistic Argumentation Machines

Neural-symbolic systems combine the strengths of neural networks and symbolic formalisms. In this paper, we introduce a neural-symbolic system which combines restricted Boltzmann machines and probabilistic semi-abstract argumentation. We propose to train networks on argument labellings explaining the data, so that any sampled data outcome is associated with an argument labelling. Argument labellings are integrated as constraints within restricted Boltzmann machines, so that the neural networks are used to learn probabilistic dependencies amongst argument labels. Given a dataset and an argumentation graph as prior knowledge, for every example/case K in the dataset, we use a so-called K-maxconsistent labelling of the graph, and an explanation of case K refers to a K-maxconsistent labelling of the given argumentation graph. The abilities of the proposed system to predict correct labellings were evaluated and compared with standard machine learning techniques. Experiments revealed that such argumentation Boltzmann machines can outperform other classification models, especially in noisy settings.

Aggregation of Perspectives Using the Constellations Approach to Probabilistic Argumentation

In the constellations approach to probabilistic argumentation, there is a probability distribution over the subgraphs of an argument graph, and this can be used to represent the uncertainty in the structure of the argument graph. In this paper, we consider how we can construct this probability distribution from data. We provide a language for data based on perspectives (opinions) on the structure of the graph, and we introduce a framework (based on general properties and some specific proposals) for aggregating these perspectives, and as a result obtaining a probability distribution that best reflects these perspectives. This can be used in applications such as summarizing collections of online reviews and combining conflicting reports.