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Attribute-level schema matching has proven to be an important first step in developing mappings for data exchange, integration, restructuring and schema evolution. In this paper we investigate contextual schema matching, in which selection conditions are associated with matches by the schema matching process in order to improve overall match quality. We define a general space of matching techniques, and within this framework we identify a variety of novel, concrete algorithms for contextual schema matching. Furthermore, we show how common schema mapping techniques can be generalized to take more effective advantage of contextual matches, enabling automatic construction of mappings across certain forms of schema heterogeneity. An experimental study examines a wide variety of quality and performance issues. In addition, it demonstrates that contextual schema matching is an effective and practical technique to further automate the definition of complex data transformations.