Towards a general theory of evidential reasoning

Abstract

This paper describes a general assignment method for combining evidences in the form of mass assignments over the power set, P (X), of a set of labels. It also describes an iterative assignment method for updating an apriori assignment over P (X) with evidences E1, ..., Er all expressed as assignments over P (X). This can be thought of as an extension of Bayesian updating with uncertain information. A minimum relative information optimisation of the updated assignment relative to the apriori is used. The methods have application to knowledge engineering for processing rules with uncertainties, causal nets and other representations for inference purposes. Solutions to the non-monotonic logic and abduction problems are special cases of this inference process. The methods are not the same as the Dempster Shafer theory of evidential reasoning, [Shafer 1976] but does use Shafer's belief function form of representing uncertainty.