On Conditional Belief Functions in the Dempster-Shafer Theory

The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similar to the notion of conditional probability tables in probability theory. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables for constructing Bayesian networks. Besides defining conditional belief functions, we state and prove a few basic properties of conditionals. We provide several examples of conditional belief functions, including those obtained by Smets’ conditional embedding.