Temporal Dependencies with Order Constraints a Timecenter Technical Report Title Temporal Dependencies with Order Constraints Author(s) Publication History Individual Participants

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<;=;>; ; ; 6=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.