The Relational Structure of Belief Networks

This paper demonstrates the relational structure of belief networks by establishing an extended relational data model which can be applied to both belief networks and relational applications. It is demonstrated that a Markov network can be represented as a generalized acyclic join dependency (GAJD) which is equivalent to a set of conflict-free generalized multivalued dependencies (GMVDs). A Markov network can also be characterized by an entropy function, which greatly facilitates the manipulation of GMVDs. These results are extensions of results established in relational theory. It is shown that there exists a complete set of inference rules for the GMVDs. This result is important from a probabilistic perspective. All the above results explicitly demonstrate that there is a unified model for relational database and probabilistic reasoning systems. This is not only important from a theoretical point of view in that one model has been developed for a number of domains, but also from a practical point of view in that one system can be implemented for both domains. This implemented system can take advantage of the performance enhancing techniques developed in both fields. Thereby, this paper serves as a theoretical foundation for harmonizing these two important information domains.