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.