  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.
