Explanation Over Inference Hierarchies in Active Mediation Applications

Abstract

This paper gives algorithms to compute the explanation of instance membership in classes over an Inference Hierarchy. O(c) time algorithms are given to compute the positive, negative, and conditional explanations over an Inference Hierarchy limited to conjunctive parents, where c is the total number of conditions in the Inference Hierarchy.¹ Algorithms requiring O(c ² k) time and space are given for computing the k-minimal positive, negative and conditional explanations over disjunctive hierarchies with independent conditions. Worst-case exponential time is required for computing negative and negative conditional explanations over disjunctive hierarchies with dependent conditions. All types of explanation are worst-case exponential time for the k-minimal explanations over hierarchies using negation in parent relationships. An application for these algorithms is provided. The application is motivated by the DARPA ALP storyboard and provides active mediation of airport facility status in a combat situation. These techniques may be transferred to financial, administrative, and environmental domains as well.