# Probabilistic argumentation

Probabilistic argumentation refers to different formal frameworks in the literature. All share the idea that qualitative aspects can be captured by an underlying logic, while quantitative aspects of uncertainty can be accounted for by probabilistic measures.

## Probabilistic labellings

The framework of "probabilistic labellings" refers to probability spaces where the sample space is a set of labellings of argumentation graphs. As a labelling of an argumentation graph associates any argument with a label to reflect the acceptability of the argument (if the labelling is total), the approach of probabilistic labellings associates an arguments with the probability of a label to reflect the probability of the argument to be labelled as such.

## Probabilistic argumentation systems

The name "probabilistic argumentation" has been used to refer to a particular theory of reasoning that encompasses uncertainty and ignorance, combining probability theory and deductive logic, and thus consisting in a probabilistic logic (Haenni, Kohlas & Lehmann 2000). OpenPAS is an open-source implementation of such a probabilistic argumentation system.

Probabilistic argumentation systems encounter a problem when used to determine the occurrence of Black Swan events since, by definition, those events are so improbable as to seem impossible. As such, probabilistic arguments should be considered fallacious arguments known as appeals to probability.

## References

• Riveret, R.; Baroni, P.; Gao, Y.; Governatori, G.; Rotolo, A.; Sartor, G. (2018), "A Labelling Framework for Probabilistic Argumentation", Annals of Mathematics and Artificial Intelligence, 83: 221–287, arXiv:1708.00109, doi:10.1007/s10472-018-9574-1
• Haenni, R.; Kohlas, J.; Lehmann, N. (2000), "Probabilistic argumentation systems" (PDF), in J. Kohlas and S. Moral (ed.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Dordrecht: Volume 5: Algorithms for Uncertainty and Defeasible Reasoning, Kluwer, pp. 221–287, archived from the original (PDF) on 2005-01-25
• D.M. Gabbay and O.Rodrigues, "Probabilistic Argumentation: An Equational Approach", Logica Universalis, 2015. doi:10.1007/s11787-015-0120-1