Extending and formalizing Bayesian networks by strong relevant logic

Abstract

In orders to deal with uncertainty by systematical methodologies, some structural models combining probability theory with logic systems have been proposed. However, these models used only the formal language part of the underlying logic system to represent empirical knowledge of target domains, but not asked the logical consequence theory part of the underlying logic system to reason about empirical theorems that are logically implied in domain knowledge. As the first step to establish a unifying framework to support uncertainty reasoning, this paper proposes a new framework that extends and formalizes traditional Bayesian networks by combining Bayesian networks with strong relevant logic. The most intrinsic feature of the framework is that it provides a formal system for representing and reasoning about generalized Bayesian networks, and therefore, within the framework, for given empirical knowledge in a specific target domain, one can reason out those new empirical theorems that are certainly relevant to given empirical knowledge. As a result, using an automated forward reasoning engine based on strong relevant logic, it is possible to get Bayesian networks semi-automatically. © 2013 Springer-Verlag.