An Ordinal View of Independence with Application to Plausible Reasoning

TL;DR

This paper explores an ordinal approach to independence within possibility theory, proposing three definitions of dependence, with one supporting the entire framework and applications to belief change and reasoning.

Contribution

It introduces three notions of independence in possibility theory, provides axiomatization for the strongest, and demonstrates applications to belief change and exception-tolerant reasoning.

Findings

Three definitions of dependence are proposed.

A complete axiomatization is provided for the strongest dependence.

Weak independence effectively addresses property inheritance blocking.

Abstract

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning.