An Ordinal View of Independence with Application to Plausible Reasoning
This work addresses foundational issues in non-probabilistic reasoning for AI and logic, offering incremental theoretical advancements.
The paper tackles the problem of defining independence in possibility theory, proposing three definitions of increasing strength and providing a complete axiomatization for the strongest one, with application to blocking property inheritance in plausible reasoning.
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.