Redescription mining is a newly introduced data mining problem that seeks to find subsets of data that afford multiple definitions. It can be viewed as a generalization of association rule mining, from finding implications to equivalences; as a form of conceptual clustering, where the goal is to identify clusters that afford dual characterizations; and as a form of constructive induction, to build features based on given descriptors that mutually reinforce each other. In this paper, we present the use of redescription mining as an important tool to reason about a collection of sets, especially their overlaps, similarities, and differences. We outline algorithms to mine all minimal (non-redundant) redescriptions underlying a dataset using notions of minimal generators of closed itemsets. We also show the use of these algorithms in an interactive context, supporting constraint-based exploration and querying. Specifically, we showcase a bioinformatics application that empowers the biologist to definea vocabulary of sets underlying a domain of genes and to reason about these sets, yielding significant biological insight.
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