We present a flexible approach for extracting hierarchical classifications from linguistic data. To this end, the framework of observational logic is introduced, which extends the logic that underlies standard Formal Concept Analysis by allowing disjunctive rules and exclusions. We give a rigorous mathematical characterization of how the chosen rule type affects the structure of the induced hierarchy. The framework is applied to the induction of hierarchical classifications from linguistic databases. The pros and cons of several types of hierarchies are discussed in detail with respect to criteria such as compactness of representation, suitability for inference tasks, and intelligibility for the human user.