This paper presents an axiomatic system for propagating uncertainty in Pearl's causal
networks, (Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference,
1988 [7]). The main objective is to study all aspects of knowledge representation
and reasoning in causal networks from an abstract point of view, independent of the
particular theory being used to represent information (probabilities, belief functions or
upper and lower probabilities). This is achieved by expressing concepts and algorithms
in terms of valuations, an abstract mathematical concept representing a piece of
information, introduced by Shenoy and Sharer [1, 2]. Three new axioms are added to
Shenoy and Shafer's axiomatic framework [1, 2], for the propagation of general
valuations in hypertrees. These axioms allow us to address from an abstract point of
view concepts such as conditional information (a generalization of conditional probabilities)
and give rules relating the decomposition of global information with the concept of
independence (a generalization of probability rules allowing the decomposition of a
bidimensional distribution with independent marginals in the product of its two
marginals). Finally, Pearl's propagation algorithms are also developed and expressed in
terms of operations with valuations.Commission of the European Communities
under ESPRIT BRA 3085: DRUM
