Practical preference relations for large data sets

User-defined preferences allow personalized ranking of query results. A user provides a declarative specification of his/her preferences, and the system is expected to use that specification to give more prominence to preferred answers. We study constraint formalisms for expressing user preferences as base facts in a partial order. We consider a language that allows comparison and a limited form of arithmetic, and show that the transitive closure computation required to complete the partial order terminates. We consider various ways of composing partial orders from smaller pieces, and provide results on the size of the resulting transitive closures. Finally, we show how preference queries within our language can be supported by suitable index structures for efficient evaluation over large data sets. Our results provide guidance about when complex preferences can be efficiently evaluated, and when they cannot.