Propagating belief functions through constraints systems

Abstract

Constraint systems as used in temporal reasoning usually describe uncertainty by constraining variables into given sets. Viewing belief functions as random or uncertain sets, uncertainty in such models is quite naturally and more generally described by belief functions. Here a special class of constraint systems induced by the additive underlying group structure is considered. Belief functions are used to specify uncertain constraints on relations and constraint propagation can be applied to compute belief functions about relations between specified events.

The computations are as usual plagued by combinatorial explosion in the general case. Structural properties of the temporal knowledge base must therefore be exploited. It is explained that there are topological properties of the graph representing the model which can be used to reduce computational complexity. Series-parallel graphs are shown to be particularly simple with respect to computations. They play a role analogous to qualitative Markov trees in multivariate models. These methods are related to the use of reference events — a technique well known in temporal reasoning — to obtain a natural hierarchical structuring of the knowledge base.