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Queries posed to database systems often involve universal quantification. Such queries are typically expensive to evaluate. Although they can be handled by basic access methods, for selection, grouping, and so forth, new access methods specifically tailored to evaluate universal quantification can greatly decrease the computational cost. In this paper, we study the efficient evaluation of universal quantification in an XML database. Specifically, we develop a small taxonomy of universal quantification types and define a family of algorithms suitable for handling each. We experimentally demonstrate the performance benefits of the new family of algorithms.