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With the advent of XML, great challenges arise from the demand for efficiently retrieving information from remote XML sources across the Internet. Recently, the advance of extensible Markup Language (XML) as the lingua franca of the Web meets the needs for an interoperable data exchange format on the Web. The semantic caching technology can help to improve the efficiency of XML query processing in the Web environment. Unlike from the traditional tuple or page-based caching systems, semantic caching systems exploit the idea of reusing cached query results to answer new queries based on the query containment and rewriting techniques. Fundamental results on the containment of relational queries have been determined. The results show that some of our measures outperform the traditional measures in certain situations.