D . Dubois , L . Fariñas Del Cerro , a . Herzig and H . Prade a Roadmap of Qualitative Independence

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; Fariñas 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, Fariñas 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 underlie major belief change and nonmonotonic inference theories. In the paper we focus on epistemic independence between events. A, B, C, . . . stand for events (propositions) belonging to a Boolean algebra of subsets of a set W . (Hence we do not distinguish between logically equivalent formulas.) T andF are propositions denoting the true and false events respectively; :A denotes the negation of proposition A, representing the complement of A in W . Let us assume that our representation framework enables us to distinguish between three cognitive attitudes regarding C: C is an accepted belief, :C is an accepted belief (i.e. C is refuted), neither C nor :C is accepted (i.e. total ignorance about C).