Uncertain Relations between Indeterminate Temporal Intervals

Time is important in modeling dynamic aspects of the world, and particularly in the temporal databases field. Many research articles about temporal databases assume that complete and accurate temporal information is available. However, in many real applications temporal information is imperfect and we need to find some way of handling it. The two main commonly used temporal ontological primitives are point and interval. Often a temporal point is indeterminate, which means that an interval of possible values for the point is given, and the probability mass function for that interval can be defined. An indeterminate temporal interval is represented as a pair of indeterminate points denoting the start and the end of the interval. Sometimes there is a need to know relations between temporal intervals, as for example, in query processing. When intervals are indeterminate, it is almost impossible to derive a certain relation between them. This paper presents an approach to estimate the uncertain relation between two indeterminate temporal intervals by calculating the probabilities of Allen’s relations. The relation between two indeterminate intervals is represented using four relations between their indeterminate endpoints. Using the information about the endpoints, we derive four uncertain relations between them, and then calculate the probabilities of Allen’s relations by the proposed formulas. We present an example of the behavior of the proposed mechanism regarding calculation complexity using different input data. We also consider an example illustrating a possible application of the approach.