Probabilistic Deduction: an Approach to Probabilistic Structured Argumentation
This work addresses the integration of probabilistic and argumentative reasoning in AI, offering a novel foundational approach that is not incremental but establishes a new framework.
The paper tackles the problem of unifying probabilistic reasoning with argumentative reasoning by introducing Probabilistic Deduction (PD), a framework that uses probabilistic rules to define joint probability distributions and perform reasoning, proving it coincides with classical argumentation under a probabilistic closed-world assumption and maximum entropy reasoning.
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.