Estimating uncertain relations between indeterminate temporal points and intervals

In many applications of temporal representation and reasoning formalisms there is a need to deal with temporal relations. Many published approaches assume that the temporal information available is precise and certain, although in reality this is not always true. Therefore, we need to find some way of handling imperfect temporal information. In this paper we propose one way to represent uncertain relations between indeterminate temporal points and intervals using a probabilistic approach. An uncertain relation is estimated by calculating the probabilities of the basic relations (<, =, > for points, and Allen's relations for intervals). We also assume that the measurements of temporal values can include some error, which needs to be taken into account when estimating an uncertain temporal relation. We suppose that the maximum value of the measurement error is known. Taking into account this error we calculate the extreme probability values of the basic relations between temporal primitives.