Belief Maintenance With Uncertainty

A. Julian Craddock and Roger A. Browse

Abstract

A framework for representing and reasoning with uncertain information is described. A network knowledge structure is used which makes the reasons for believing or not believing a proposition explicit. These reasons, or endorsements, are quantified by a measure of belief and certainty. Heuristics are integrated with the knowledge structure to collect, and evaluate the endorsements.

Introduction

The research reported in this paper pursues the problem of developing representational and inference mechanisms which are capable of dealing with incomplete, inaccurate, and uncertain information. The direction taken is based on the assumption that methods which deal effectively with uncertainty must play an integral role in both models of human reasoning, and flexible computational reasoning systems.

Most formal reasoning systems combine both the extent of belief and certainty of belief into a single truth value, whether binary or multi-valued (McCarthy 1980; McDermott and Doyle 1980; Reiter 1978a; Zadeh 1983). In many cases, this compression is justified, but consider the proposition RICK LIKES MATH. The extent of belief in this proposition may be high whether it is quite certain (Rick has taken, and enjoyed a wide range of math courses) or quite uncertain (Rick has only taken a single math course).

Recently Cohen (1983) has formulated a model of reasoning which maintains that reasons for believing or disbelieving propositions can be collected, providing a more comprehensive description of belief. Our approach is to employ a knowledge structure such that these reasons, or endorsements, are made explicit. The endorsements for propositions can be quantified by a measure of belief and certainty. In addition, a network of endorsements among propositions may be used to: (1) determine how supportive a body of evidence for a particular hypothesis is and (2) represent evidential relationships such as conflicts between decisions (Craddock 1986).

The algorithms which compute the belief and certainty of a proposition may be formulated to operate uniformly on all supporting knowledge, or the algorithms may be subject to heuristics which emphasize the importance of selected portions of the supporting knowledge. In the development of heuristic methods we have been guided by the approach taken by Kahneman and Tversky (1982a,b). Their model indicates that humans employ a set of basic heuristics which aid in making decisions in conditions of uncertainty. These heuristics enable humans to constrain problem domains such that the uncertainty becomes manageable but still useful. In addition humans can also employ heuristics to determine complex evidential relationships between different sources of evidence.