Possibilistic Conditioning and Propagation

TL;DR

This paper axiomatizes confidence transfer in possibilistic conditioning, evaluates various rules using belief independence, and demonstrates a local computation scheme derived from independence assumptions, aligning with Bayesian principles.

Contribution

It introduces an axiomatization of confidence transfer, identifies Dempster's rule as supporting belief independence, and derives a local computation scheme from independence assumptions.

Findings

Dempster's rule supports belief independence

Local computation scheme derived from independence assumptions

Comparison with Shenoy's valuation-based systems

Abstract

We give an axiomatization of confidence transfer - a known conditioning scheme - from the perspective of expectation-based inference in the sense of Gardenfors and Makinson. Then, we use the notion of belief independence to "filter out" different proposal s of possibilistic conditioning rules, all are variations of confidence transfer. Among the three rules that we consider, only Dempster's rule of conditioning passes the test of supporting the notion of belief independence. With the use of this conditioning rule, we then show that we can use local computation for computing desired conditional marginal possibilities of the joint possibility satisfying the given constraints. It turns out that our local computation scheme is already proposed by Shenoy. However, our intuitions are completely different from that of Shenoy. While Shenoy just defines a local computation scheme that fits his framework of valuation-based systems, we derive that local computation scheme from II(,8) = tI(,8 I a) * II(a) and appropriate independence assumptions, just like how the Bayesians derive their local computation scheme.