Hierarchical censored production rules (HCPRs) system employing the dempster-shafer uncertainty calculus

Abstract

This paper addresses the problem of reasoning under time constraints with incomplete and uncertain information. It is based on the idea of Variable Precision Logic (VPL), introduced by Michalski and Winston. The approach taken is to vary the precision of inferences in order to produce the most accurate answer possible within a given time limit. VPL deals with both the problem of reasoning with incomplete information subject to time constraints and the problem of reasoning efficiently with exceptions. It offers mechanisms for handling trade-offs between the precision of inferences and the computational efficiency of deriving them. The two aspects of precision are the certainty of belief and the specificity of conclusion in them. Michalski and Winston suggested the Censored Production Rule (CPR) as an underlying representational and computational mechanism to enable logic-based systems to exhibit variable precision in which certainty varies while specificity stays constant. CPRs are obtained by augmenting ordinary production rules with an exception condition and are written as ‘if A then B unless C’, where C is the exception condition. Such rules are employed in situations in which the conditional statement ‘if A then B' holds frequently and the assertion C holds rarely. By using a rule of this type we are free to ignore the exception condition, when the resources needed to establish its presence are tight or there simply is no information available as to whether it holds or does not hold. Thus ‘if A then B’ part of the CPR expresses important information while the ‘unless C’ part acts only as a switch that changes the polarity of B to B when C holds. As an extension of CPR, a Hierarchical Censored Production Rules (HCPRs) system of knowledge representation proposed by Bharadwaj and Jain exhibits both variable certainty as well as variable specificity. The work presented in this paper addresses the problem of handling uncertainty in the HCPRs system based on the ideas of Dempster-Shafer uncertainty calculus. The use of Dempster-Shafer Theory to formalize VPL type inference provides a simple, intuitive notion of the precision of an inference which relates it to the amount of information found. This formalism allows the ignorance in the evidence to be preserved through the reasoning process and expressed in the decision. To make the HCPRs system more effective specialized combination and propagation functions for reasoning in taxonomies are developed and thereby two different reasoning schemes for HCPRs system are presented. Examples are given to demonstrate the behaviour of the proposed schemes.