Combining Symbolic and Numeric Approaches to Uncertainty Management

TL;DR

This paper introduces a hybrid reasoning scheme combining symbolic ATMS techniques with numeric Dempster/Shafer evidence methods to improve uncertainty management, enabling dynamic hypothesis space determination and incremental model revision.

Contribution

It presents a novel hybrid approach that integrates symbolic and numeric uncertainty reasoning, enhancing efficiency and flexibility over traditional methods.

Findings

Faster runtime evaluation of propositional certainties

Improved management of dependent and independent evidence

Supports incremental model extension and revision

Abstract

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.