A Logical Approach to Data-Driven Classification

We present a flexible approach for extracting hierarchical classifications from data, which employs the logic of affirmative assertions. The basic observation is that each set of rules induced by the data canonically determines a classificational hierarchy. We give a characterization of how the chosen rule type affects the structure of the induced hierarchy. Moreover, we show how our approach is related to Formal Concept Analysis. The framework is then applied to the induction of hierarchical classifications from an amino acid database. Based on this example, the pros and cons of several types of hierarchies are discussed with respect to criteria such as compactness of representation, suitability for inference tasks, and intelligibility for the human user.