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Peculiarity rules are a new class of rules which can be discovered by searching relevance among a relatively small number of peculiar data. Peculiarity oriented mining in multiple data sources is different from, and complementary to, existing approaches for discovering new, surprising, and interesting patterns hidden in data. A theoretical framework for peculiarity oriented mining is presented. Within the proposed framework, we give a formal interpretation and comparison of three classes of rules, namely, association rules, exception rules, and peculiarity rules, as well as describe how to mine interesting peculiarity rules in multiple databases.