Combining Symbolic and Numeric Approaches to Uncertainty Management
  A complete approach to reasoning under uncertainty requires support for
incremental and interactive formulation and revision of, as well as reasoning
with, models of the problem domain capable of representing our uncertainty. We
present a hybrid reasoning scheme which combines symbolic and numeric methods
for uncertainty management to provide efficient and effective support for each
of these tasks. The hybrid is based on symbolic techniques adapted from
Assumption-based Truth Maintenance systems (ATMS), combined with numeric
methods adapted from the Dempster/Shafer theory of evidence, as extended in
Baldwin's Support Logic Programming system. The hybridization is achieved by
viewing an ATMS as a symbolic algebra system for uncertainty calculations. This
technique has several major advantages over conventional methods for performing
inference with numeric certainty estimates in addition to the ability to
dynamically determine hypothesis spaces, including improved management of
dependent and partially independent evidence, faster run-time evaluation of
propositional certainties, the ability to query the certainty value of a
proposition from multiple perspectives, and the ability to incrementally extend
or revise domain models.
