Probabilistic Estimation of Uncertain Temporal Relations

A wide range of AI applications should manage time varying information, for example, temporal databases, reservation systems, keeping medical records, financial applications, planning. Many published research articles in the area of temporal representation and reasoning assume that temporal data is precise and certain, even though in reality this assumption is often false. In many situations there is a need to know the relation between two temporal intervals, as it is, for example, during query processing. Indeterminacy means that we do not know exactly when a particular event happened. When two temporal intervals are indeterminate it is in many cases impossible to derive a certain temporal relation between them. In this paper we propose an approach to represent and estimate uncertain temporal relations by calculating the probabilities of the basic relations that can hold between two temporal primitives. We represent the relation between two temporal intervals as a matrix, four elements of which are the relations between the endpoints of these intervals. The uncertain relation between two temporal points is represented by a vector with three probability values denoting the probabilities of the basic relations (before, at the same time, after) between these points. The probabilities of Allen’s interval relations between two temporal intervals are composed as joint conditional probabilities of the correspondent relations between the endpoints of the intervals. We also consider an example of using the proposed estimation mechanism, which helps to figure out possible application areas of the formalism.