Three-Valued Possibilistic Networks: Semantics & Inference

Possibilistic networks are belief graphical models based on possibility theory. This paper deals with a special kind of possibilistic networks called three-valued possibilistic networks where only three possibility levels are used to encode uncertain information. The paper analyzes different semantics of three-valued networks and provides precise relationships relating the different semantics. More precisely, the paper analyzes two categories of methods for deriving a three-valued joint possibility distribution from a three-valued possibilistic network. The first category of methods is based on viewing a three-valued possibilistic network as a family of compatible networks and defining combination rules for deriving the three-valued joint distribution. The second category is based on three-valued chain rules using three-valued operators inspired from some three-valued logics. Finally, the paper shows that the inference using the well-known junction tree algorithm can only be extended for some three-valued chain rules.