A roadmap of qualitative independence
Résumé
The notion of epistemic independence naturally arises in the framework of reasoning under uncertainty and belief change. Most prominently, probabilistic conditional independence (between variables) plays a key role in Bayesian nets. Several authors [Delgrande and Pelletier, 1994; Benferhat et al., 1994; Dubois et al., 1994; Farinas del Cerro and Herzig, 1995] have advocated the interest of qualitative independence notions for nonmonotonic reasoning. Gärdenfors [1990] has investigated the complementary notion of relevance in relation with belief change; continuing in this spirit, Farinas del Cerro and Herzig [1996] have related independence and belief contraction. In the framework of possibility theory, new forms of independence between variables have been studied by Fonck [1993], and De Campos et al. [1995], who develop possibilistic counterparts of Bayesian nets. The aim of the paper is to provide an exhaustive typology of the forms that independence and relevance can take in the setting of an ordinal approach to uncertainty. Such an approach underlies major belief change and nonmonotonic inference theories.