— Uncertainties in data arise for a number of reasons: when the data set is incomplete, contains conflicting information or has been deliberately perturbed or coarsened to remove sensitive details. An important case which arises in many real applications is when the data describes a set of possibilities, but with cardinality constraints. These constraints represent correlations between tuples encoding, e.g. that at most two possible records are correct, or that there is an (unknown) one-to-one mapping between a set of tuples and attribute values. Although there has been much effort to handle uncertain data, current systems are not equipped to handle such correlations, beyond simple mutual exclusion and co-existence constraints. Vitally, they have little support for efficiently handling aggregate queries on such data. In this paper, we aim to address some of these deficiencies, by introducing LICM (Linear Integer Constraint Model), which can succinctly represent many types of tuple...