Exploiting functional dependencies in qualitative probabilistic reasoning

Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and mod­ ifying the inference rules to produce stronger conclusions in the presence of functional rela­ tions. I describe how to accomplish these modi­ fications in qualitative probabilistic networks by exhibiting the update procedures for graphical transformations involving probabilistic and de­ terministic variables and combinations. A sim­ ple example demonstrates that the augmented scheme can reduce qualitative ambiguity that would arise without the special treatment of functional dependency. Analysis of qualitative synergy reveals that new higher-order relations are required to reason effectively about syn­ ergistic interactions among deterministic vari­ ables.