AN AXIOMATIC FRAMEWORK FOR PROPAGATING UNCERTAINTY IN DIRECTED ACYCLIC NETWORKS

This paper presents an axiomatic system for propagating uncertainty in Pearl's causal networks, (Probabilistic Reasoning in Intelligent Syst ems: Networks of Plausible Inference, 1988 [7]). The main objective is to study all aspects of knowledge representation and reasoning in cau sal networks from an abstract point of view, independent of the partic ular theory being used to represent information (probabilities, belief functions or upper and lower probabilities). This is achieved by expr essing concepts and algorithms in terms of valuations, an abstract mat hematical concept representing a piece of information, introduced by S henoy and Shafer [1, 2]. Three new axioms are added to Shenoy and Shaf er's axiomatic framework [1, 2], for the propagation of general valuat ions in hypertrees. These axioms allow us to address from an abstract point of view concepts such as conditional information (a generalizati on of conditional probabilities) and give rules relating the decomposi tion of global information with the concept of independence (a general ization of probability rules allowing the decomposition of a bidimensi onal distribution with independent marginals in the product of its two marginals). Finally, Pearl's propagation algorithms are also develope d and expressed in terms of operations with valuations.