Uncertainty and Incompleteness

Abstract: 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.