Complex systems consist of collections of interacting processes. These processes change over time in response to both internal and external stimuli as well as to the passage of time itself. There is great variety in the behavior of processes. Some processes are simple events such as going to lunch or flipping a switch. Others are complex. One example being a communication channel, in which errors may occur due to lightning strikes and in which errors are more likely following previous errors. Processes can also be recurrent or periodic, such as the passing of day into night or shifts in a work schedule.
Prior temporal modeling techniques have often had difficulty modeling uncertainty as to when and if an event occurs. Techniques able to model uncertainty often do not have strong semantics. One such method, the Temporal Abduction Problem (TAP) of [4] uses a cost based approach to model the uncertainty in an events occurrence, however the costs are adhoc and TAP does not model the uncertainty as to when the event happened or for how long.
Bayesian networks [2] provide a robust, probabilistic method of reasoning with uncertainty which has become popular with artificial intelligence researchers. Bayesian networks, however, do not provide a direct mechanism for representing temporal dependencies. For example, it is difficult to represent a situation such as the variability of when an employee arrives at work and the causal relationships between the time of arrival and later events.
This paper presents a new system, the Temporal Bayesian Network (TBN), for representing temporal and atemporal information while maintaining probabilistic semantics. The technique allows representation of time constrained causality, of when and if events occur, and of the periodic and recurrent nature of processes. Bayesian networks lie at the foundation of the system and provide the probabilistic basis. Allen's interval system [1] and his 13 relations provide the temporal basis.