Modeling temporal processes via belief networks and Petri nets,with application to expert systems

We show how Bayesian belief networks (BNs) can be used to model common temporal knowledge. Two approaches to their structuring are proposed. The first leads to BNs with nodes representing states of a process and times spent in such states, and with a graphical structure reflecting the conditional independence assumptions of a Markovian process. A second approach leads to BNs whose topology represents a conditional independence structure between event-times. Once required distributional specifications are stored within the nodes of a BN, this becomes a powerful inference machine capable, for example, of reasoning backwards in time. We discuss computational difficulties associated with propagation algorithms necessary to perform these inferences, and the reasons why we chose to adopt Monte Carlo-based propagation algorithms. Two improvements to existing Monte Carlo algorithms are proposed; an enhancement based on the principle of importance sampling, and a combined technique that exploits both forward and Markov sampling. Finally, we consider Petri nets, a very interesting and general representation of temporal knowledge. A combined approach is proposed, in which the user structures temporal knowledge in Petri net formalism. The obtained Petri net is then automatically translated into an equivalent BN for probability propagation. Inferred conclusions may finally be explained with the aid of Petri nets again.