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Data integration has been an important area of research for several years. In this paper, the authors argue that supporting modern data integration applications require systems to handle uncertainty at every step of integration. They provide a formal framework for data integration systems with uncertainty. They define probabilistic schema mappings and probabilistic mediated schemas, show how they can be constructed automatically for a set of data sources, and provide techniques for query answering. The foundations laid out in this paper enable bootstrapping a pay-as-you-go integration system completely automatically.
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