  Two major difficulties in using default logics are their intractability and
the problem of selecting among multiple extensions. We propose an approach to
these problems based on integrating nommonotonic reasoning with plausible
reasoning based on triangular norms. A previously proposed system for reasoning
with uncertainty (RUM) performs uncertain monotonic inferences on an acyclic
graph. We have extended RUM to allow nommonotonic inferences and cycles within
nonmonotonic rules. By restricting the size and complexity of the nommonotonic
cycles we can still perform efficient inferences. Uncertainty measures provide
a basis for deciding among multiple defaults. Different algorithms and
heuristics for finding the optimal defaults are discussed.
