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Current approaches for answering queries with imprecise constraints require user-specific distance metrics and importance measures for attributes of interest - metrics that are hard to elicit from lay users. We present AIMQ, a domain and user independent approach for answering imprecise queries over autonomous Web databases. We developed methods for query relaxation that use approximate functional dependencies. We also present an approach to automatically estimate the similarity between values of categorical attributes. Experimental results demonstrating the robustness, efficiency and effectiveness of AIMQ are presented. Results of a preliminary user study demonstrating the high precision of the AIMQ system is also provided.