Combining Symbolic and Numeric Approaches to Uncertainty Management

Uncertainty is represented in an Assumption-based Truth Maintenance System (ATMS) by tokens called cusumptions, which are used to represent belief in uncertain facts. Given a set of assumptions and a set of inferences which can be drawn from these assumptions and their consequents, the ATMS derives a complete boolean expression (label) for the truth value of every proposition in the database, expressed in terms of the original assumption tokens. Thus, an ATMS can be viewed as a symbolic algebra system for uncertainty reasoning. Previously, assumptions have always been taken to be truth variables ranging over boolean truth values. This paper describes a method of attaching numeric certainty estimates to assumptions, and deriving numeric truth values from the labels of ATMS propositions. This technique has several major advantages over conventional methods for performing inference with numeric certainty estimates, including improved management of dependent and partially independent evidence, faster run-time evaluation of propositional certainties, and the ability to query the certainty value of a proposition from multiple perspectives.