  There currently exists a gap between the theories proposed by the probability
and uncertainty and the needs of Artificial Intelligence research. These
theories primarily address the needs of expert systems, using knowledge
structures which must be pre-compiled and remain static in structure during
runtime. Many Al systems require the ability to dynamically add and remove
parts of the current knowledge structure (e.g., in order to examine what the
world would be like for different causal theories). This requires more
flexibility than existing uncertainty systems display. In addition, many Al
researchers are only interested in using "probabilities" as a means of
obtaining an ordering, rather than attempting to derive an accurate
probabilistic account of a situation. This indicates the need for systems which
stress ease of use and don't require extensive probability information when one
cannot (or doesn't wish to) provide such information. This paper attempts to
help reconcile the gap between approaches to uncertainty and the needs of many
AI systems by examining the control issues which arise, independent of a
particular uncertainty calculus. when one tries to satisfy these needs. Truth
Maintenance Systems have been used extensively in problem solving tasks to help
organize a set of facts and detect inconsistencies in the believed state of the
world. These systems maintain a set of true/false propositions and their
associated dependencies. However, situations often arise in which we are unsure
of certain facts or in which the conclusions we can draw from available
information are somewhat uncertain. The non-monotonic TMS 12] was an attempt at
reasoning when all the facts are not known, but it fails to take into account
degrees of belief and how available evidence can combine to strengthen a
particular belief. This paper addresses the problem of probabilistic reasoning
as it applies to Truth Maintenance Systems. It describes a belief Maintenance
System that manages a current set of beliefs in much the same way that a TMS
manages a set of true/false propositions. If the system knows that belief in
fact is dependent in some way upon belief in fact2, then it automatically
modifies its belief in facts when new information causes a change in belief of
fact2. It models the behavior of a TMS, replacing its 3-valued logic (true,
false, unknown) with an infinite valued logic, in such a way as to reduce to a
standard TMS if all statements are given in absolute true/false terms. Belief
Maintenance Systems can, therefore, be thought of as a generalization of Truth
Maintenance Systems, whose possible reasoning tasks are a superset of those for
a TMS.
