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Probabilistic Temporal Network for Numeric and Symbolic Time Information
Abstract
We propose a probabilistic extension of Allen’s Interval Algebra for managing uncertain temporal relations. Although previous work on various uncertain forms of quantitative and qualitative temporal networks have been proposed in the literature, little has been addressed to the most obvious type of uncertainty, namely the probabilistic one. More precisely, our model adapts the probabilistic Constraint Satisfaction Problem (CSP) framework in order to handle uncertain symbolic and numeric temporal constraints. In a probabilistic CSP, each constraint C is given a probability of its existence in the real world. There is thus more than one CSP to solve as opposed to the traditional CSP where no such uncertainties exist. In a probabilistic temporal CSP, since we use the Interval Algebra where a constraint is a disjunction of Allen primitives, the probability is assigned to each of these Allen primitives rather than to the temporal constraint. This means that a probabilistic temporal CSP involves many possible temporal CSPs, each with a probability of its existence. Solving a probabilistic temporal CSP consists of finding a scenario that has the highest probability to be the solution for the real world. This is an optimization problem that we solve using a branch and bound algorithm we propose and involving constraint propagation. Experimental study conducted on randomly generated temporal problems demonstrates the efficiency in time of our solving method. In the case of uncertain numeric constraints, our TemPro framework for handling numeric and symbolic temporal constraints is extended to handle uncertain domains. An algorithm for dividing domains into non-overlapping areas is proposed. This algorithm guarantees that the generated possible worlds do not intersect. Probable worlds are then constructed by combining these areas. A new branch and bound algorithm, we propose, is finally applied to find the most robust solution.
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