Modelling Uncertain Implication Rules Theory

Often knowledge from human experts is expressed in the form of uncertain implication rules, such as "if A then B" with a certain degree of confidence. Therefore, it is important to include such a representation of knowledge into the process of reasoning under uncertainty. Incorporating inference rules based on the material implication of propositional logic into the evidence theory framework (e.g. Dempster-Shafer, Smets,
Dezert-Smarandache theory etc.) is conceptually simple, which is not the case with classical probability theory. In this paper, a transformation for converting uncertain implication rules into an evidence theory framework will be presented and it will be shown that it satisfies the main properties of logical implication,
namely reflexivity, transitivity and contrapositivity.