Conditional independence relations in possibility theory

The goal of this paper is to survey and briefly discuss various rules of conditioning proposed in the framework of possibility theory, as well as various conditional independence relations suggested for these rules. These conditioning rules and conditional independence relations are confronted with formal properties of conditional independence. Special attention is paid to the conditioning in the sense of a measure-theoretic approach (based on the notion of a t-norm) recently introduced by de Cooman. It is shown that this approach to conditioning and the related conditional independence notion generalizes and unifies some of the previously suggested rules and conditional independence relations. The properties of the proposed conditional independence relation completely correspond to those possessed by stochastic conditional independence.