Updating with Belief Functions, Ordinal Conditioning Functions and Possibility Measures

TL;DR

This paper explores methods for updating uncertainty measures like belief functions, possibility measures, and ordinal conditional functions across different frameworks, highlighting new Jeffrey-like conditioning rules and their relationships.

Contribution

It introduces Jeffrey-like conditioning rules in possibility theory, compares Spohn's epistemic states with possibility measures, and reinterprets Shenoy's combination rule within this context.

Findings

Jeffrey-like conditioning rules are developed for possibility theory.

Spohn's model is related to and contrasted with possibility theory.

Shenoy's combination rule has a corresponding possibilistic interpretation.

Abstract

This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart.