Graphical inference in qualitative probabilistic networks

Qualitative probabilistic networks (QPNs) are abstractions of influence diagrams that encode constraints on the probabilistic relation among variables rather than precise numeric distributions. Qualitative relations express monotonicity constraints on direct probabilistic relations between variables or on interactions among the direct relations. Like their numeric counterpart, QPNs facilitate graphical inference: methods for deriving qualitative relations of interest via graphical transformations of the network model. However, query processing in QPNs exhibits, computational properties quite different from basic influence diagrams. In particular, the potential for information loss due to the incomplete specification of probabilities poses the new challenge of minimizing ambiguity. Analysis of the properties of QPN transformations reveals several characteristics of admissible graphical inference procedures.