Independence in conditional possibility theory

This chapter proposes a notion of independence in the conditional possibility theory, which encompasses the critical situations presented by other independence definitions. The conditional possibility is directly defined as a function on a set (with a suitable algebraic structure) of conditional events, in such a way that π (. E|H) makes sense for any pair of events E and H, with H ≠ Ø, and it must satisfy proper axioms. A characterization theorem of conditional possibility in terms of a class of unconditional possibility measures allows introducing a new notion of independence, which is a formal counterpart of stochastic independence in the framework of coherent conditional probability. The proposed independence notion can be generalized to conditional independence among random variables. © 2006 Copyright © 2006 Elsevier B.V. All rights reserved..