Probabilistic Deduction: an Approach to Probabilistic Structured Argumentation

TL;DR

This paper introduces Probabilistic Deduction (PD), a novel framework for probabilistic structured argumentation that unifies probabilistic reasoning with argumentation, using p-rules to define joint distributions and reasoning processes.

Contribution

It presents the first probabilistic structured argumentation framework where joint distributions are derived internally from p-rules, integrating probabilistic and argumentative reasoning.

Findings

PD coincides with classical argumentation under P-CWA

PD aligns with maximum entropy reasoning

Provides practical methods for computing joint distributions

Abstract

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.