Approximate predicates can be used to reduce the number of comparisons made by expensive, complex predicates. For example, to check if a point is within a region (expensive predicate) we can first check if the point is within a bounding rectangle (approximate predicate). In general, approximate predicates may have false positive and false negative errors. In this paper we study the problem of selecting and structuring approximate predicates in order to reduce the cost of processing a user

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... while keeping errors within user-specified bounds. We model different types of approximate predicates and their dependencies, we derive expressions for the errors of compound predicates, and we develop query optimization strategies. We also study the complexity of our optimization strategies under various scenarios, and we present an experimental case study that illustrates the potential gains achieved by optimizing queries with approximate predicates.