Probabilistic reasoning about uncertain relations between temporal points

A wide range of AI applications should manage time varying information. 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. However, in many real applications temporal information is imperfect and there is a need to find some way of handling it. An uncertain relation between two temporal points is represented as a vector with three probability values denoting the probabilities of the three basic relations: "<" (before), "=" (at the same time), and ">" (after). The reasoning mechanism includes inversion, composition, addition, and negation operations. We propose formulas to calculate the probability values within the uncertainty vectors representing the resulting relations of the reasoning operations. We also consider an example of using the proposed representation and reasoning mechanism.