Time Intervals

To represent this input information and the diagnostic conclusions we need a representation for the temporal properties of the instantiated nodes. This is accomplished by representing the truth of a finding or node over a temporal interval. For example, the chest pain is true over . Unfortunately, with varying delays, onsets, and persistences the diagnostic conclusions from the findings are not as definite and require indefinite time bounds to specify the ends of the intervals. For example, if pneumonia is responsible for the pulmonary congestion, the pneumonia could be true now or could have ended in the last day, since it may take up to a day for the rales to clear. Furthermore, the pneumonia must have started within the last two weeks, otherwise it would be over by now. It must have started a couple of days ago for the effects to be present now. Deductions such as these can be captured by time intervals that have four time parameters: earliest beginning, latest beginning, earliest ending, and latest ending. For the pneumonia this can be represented as: .

This representation of time is not completely sufficient for reasoning because it loses some information. In general, it is not possible to determine the minimum and maximum extent of the node from the interval. In the case of pneumonia, it lasts two days to two weeks. This information is needed to rule out certain findings as effects, or in the case of other nodes to rule out possible causes. Since the interval refers to a node or finding and that information is already in the knowledge base, including it in the temporal interval structure is a matter of computational convenience rather than necessity. Another such piece of information is the causal relationship between nodes. If the interval only places the node in the last week and another node has similar bounds, it is not possible to tell whether one can be the cause of the other. Such questions must be answered by deduction from the causal networks of the two nodes. Thus, the four parameter time interval representation provides the information needed to carry out the temporal reasoning.

In diagnosis the most common reasoning step is to infer a cause from an effect. Given the time intervals and the node representations, the determination of the time interval of the cause proceeds as follows:

Where is the earliest begin time, the latest begin time, the earliest end time, the latest end time, the delay (which includes the onset time), the onset, and the persist time. The subscripts are for the cause and for the effect. Since delay, onset, and persist are ranges, the maximum and minimum delays are used as appropriate. The reason the maximum and minimum onsets of the causes are used, instead of the opposite, is the observation that slow causes produce slow effects. The times are all temporal distances before the current time, so is two days prior to the reference time.

These time interval values must be modified to account for the max-exist of the cause, if there is one. This is a further constraint that can make the earliest begin time later (shorter time) or the latest end time earlier. If is the max-exist, then and . Therefore, and . The additional constraint that observation of cause precedes observation of effect implies that and . That they are overlapping implies and . Once the parameters of the time interval have been adjusted for these constraints, it is as exactly specified as is possible.