# Probabilistic Deduction: an Approach to Probabilistic Structured Argumentation

arXiv: https://arxiv.org/abs/2209.00210 · HTML: https://mlsanity.com/paper/2209.00210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 64 references that are in the map.
- First posted on arXiv 1 Sep 2022.

## Builds on (most cited first, 2 of 2)

- [Argumentative XAI: A Survey](https://mlsanity.com/paper/2105.11266/) (2021)
- [Epistemic Graphs for Representing and Reasoning with Positive and Negative Influences of Arguments](https://mlsanity.com/paper/1802.07489/) (2018)

## Abstract (arXiv)

This paper introduces Probabilistic Deduction (PD) as an approach to probabilistic structured argumentation. A PD framework is composed of probabilistic rules (p-rules). As rules in classical structured argumentation frameworks, p-rules form deduction systems. In addition, p-rules also represent conditional probabilities that define joint probability distributions. With PD frameworks, one performs probabilistic reasoning by solving Rule-Probabilistic Satisfiability. At the same time, one can obtain an argumentative reading to the probabilistic reasoning with arguments and attacks. In this work, we introduce a probabilistic version of the Closed-World Assumption (P-CWA) and prove that our probabilistic approach coincides with the complete extension in classical argumentation under P-CWA and with maximum entropy reasoning. We present several approaches to compute the joint probability distribution from p-rules for achieving a practical proof theory for PD. PD provides a framework to unify probabilistic reasoning with argumentative reasoning. This is the first work in probabilistic structured argumentation where the joint distribution is not assumed form external sources.