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Frequent Item set Mining (FISM) attempts to find large and frequent item sets in bag-of-items data such as retail market baskets. Such data has two properties that are not naturally addressed by FISM: (i) a market basket might contain items from more than one customer intent(mixture property) and (ii) only a subset of items related to a customer intent are present in most market baskets (projection property). We propose a simple and robust framework called LOGICAL ITEMSET MINING (LISM) that treats each market basket as a mixture-of, projections-of, latent customer intents. LISM attempts to discover logical item sets from such bag-of-items data. Each logical item set can be interpreted as a latent customer intent in retail or semantic concept in text tagsets. While the mixture and projection properties are easy to appreciate in retail domain, they are present in almost all types of bag-of-items data. Through experiments on two large datasets, we demonstrate the quality, novelty, and action ability of logical item sets discovered by the simple, scalable, and aggressively noise-robust LISM framework. We conclude that while FISM discovers a large number of noisy, observed, and frequent item sets, LISM discovers a small number of high quality, latent logical item sets.