The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices

TL;DR

This paper explores how belief updates in the Transferable Belief Model can be understood through specialization and generalization matrices, linking Dempster's rules to minimal commitment principles.

Contribution

It introduces a formal framework using specialization and generalization matrices to analyze belief updates and clarifies the foundations of Dempster's rules within this context.

Findings

Dempster's conditioning aligns with minimal commitment specialization.

Dempster's combination rule arises from commutativity constraints.

The paper formalizes the concepts of specialization and generalization in belief updating.

Abstract

The fundamental updating process in the transferable belief model is related to the concept of specialization and can be described by a specialization matrix. The degree of belief in the truth of a proposition is a degree of justified support. The Principle of Minimal Commitment implies that one should never give more support to the truth of a proposition than justified. We show that Dempster's rule of conditioning corresponds essentially to the least committed specialization, and that Dempster's rule of combination results essentially from commutativity requirements. The concept of generalization, dual to thc concept of specialization, is described.