Figure 1: An implication, A => B, being applied to an influence of A->B.
Report: Abstract
In this paper a model is proposed that combines Bayesian Networks and Propositional Logic, called an Implicative Bayesian Network (IBN). The goal of the project was to create a more expressive way to represent inferential systems, while maintaining the ability to use the well-established algorithms synonymous with both classical reasoning and Bayesian reasoning. The model was then extended with defeasible structures, which allows the model to perform non-monotonic reasoning. This paper also provides background information in the relevant fields, including an overview of logical implication and entailment in propositional logic, non-monotonic reasoning and Bayesian Networks. The paper then describes how to integrate propositional logic into a Bayesian Network, and includes new definitions, proofs, descriptions of the various relationships and properties that exist in an IBN, as well as the algorithm to transform a Bayesian Network into an IBN via a propositional logic knowledge base. To extend the IBN model to be able to perform non-monotonic reasoning, details are outlined about how the model should transform in structure. Descriptions of the new formalisms and procedures required for the extension are also provided. It is identified that further research into the properties of the construction could improve the model and its versatility. In conclusion, the basis for the model is sound, and provides a new and intuitive way to model intelligent systems.