Temporal Dependencies with Order Constraints

We propose a temporal dependency called trend dependency TD which captures a signi cant family of data evolution regularities A simple example of such regularity might be Salaries of employees do not decrease TDs compare attributes over time using operators of f g We de ne a satis ability problem that is the dual of the logical implication problem for TDs and we investigate the computational complexity of both problems We provide an axiomatization of logical implication As TDs allow expressing meaningful trends mining them from existing databases is interesting For the purpose of TD mining TD satisfaction is characterized by the common notions of support and con dence We study the problem TDMINE Given a temporal database mine the TDs that conform to a given template and whose support and con dence exceed certain threshold values The complexity of TDMINE is studied as well as algorithms to solve it A comparison with related work is provided at the end of the paper We show that TDs can express several temporal dependencies found in the literature

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