Probabilistic quantitative temporal reasoning

Temporal reasoning, in the form of propagation of temporal constraints, is an important topic in Artificial Intelligence. The current literature in the area is moving from the treatment of "crisp" temporal constraints to fuzzy or probabilistic constraints, to account for different forms of uncertainty and\or preferences. However, despite the huge amount of work in the area, the spectrum of possible solutions has not been fully explored. In particular, no probabilistic approach coping with quantitative temporal constraints has been proposed yet. We overcome such a limitation of the current literature by proposing the first approach providing (i) a probabilistic extension to quantitative constraints, supporting the possibility of expressing alternative distances between time points, and of associating a probability to each alternative, and (ii) a framework for the propagation of such temporal constraints.