A Comparative Study of Noncontextual

There is current interest in generalizing Bayesian networks by using dependencies which are more general than probabilistic conditional independence (CI). Contextual dependencies, such as context-speciic independence (CSI), are used to decompose a subset of the joint distribution. We have introduced a more general contextual dependency than CSI, as well as a more general noncontextual dependency than CI. We developed these probabilistic dependencies based upon a new method of expressing database dependencies. By deening database dependencies using equivalence relations, the diierence between the various contextual and noncontextual dependencies can be easily understood. Moreover, this new representation of dependencies provides a convenient tool to readily derive other results.