Discounting and Combination Operations in Evidential Reasoning

TL;DR

This paper explores fundamental operations in evidential reasoning, specifically the discount and orthogonal sum operations, analyzing their properties and interactions within AI evidential frameworks.

Contribution

It provides a detailed analysis of two basic evidential operations, revealing their non-commutative nature and deriving formulas for their application.

Findings

Discount operation is not commutative with orthogonal sum.

Derived expressions for operations on evidential functions.

Clarified the mathematical properties of key evidential operations.

Abstract

Evidential reasoning is now a leading topic in Artificial Intelligence. Evidence is represented by a variety of evidential functions. Evidential reasoning is carried out by certain kinds of fundamental operation on these functions. This paper discusses two of the basic operations on evidential functions, the discount operation and the well-known orthogonal sum operation. We show that the discount operation is not commutative with the orthogonal sum operation, and derive expressions for the two operations applied to the various evidential function.