Uncertainty and Incompleteness

TL;DR

This paper introduces an approach combining nonmonotonic and plausible reasoning using triangular norms to address intractability and extension selection in default logics, extending the RUM system for better handling of cycles and uncertainty.

Contribution

It extends the RUM system to incorporate nonmonotonic inferences and cycles, improving reasoning efficiency and decision-making among multiple defaults.

Findings

Extended RUM to handle cycles and nonmonotonic inferences

Proposed algorithms for selecting optimal defaults

Maintained efficiency with restricted cycle complexity

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.