When investigating objects of various types, the observations can often be presented as assignments of values to observational variables. A common task is to derive, from observations regarding known objects, a model that is able to classify objects of unknown type. Another use case is the extraction of knowledge: Based on the observations, the identification of relationships between the variables may give the observer insights into the problem domain. If the detected relations capture the essence of the data and may replace it, the discovery process can also be viewed as data compression. In this paper, we approach the tasks above from a logical perspective. We present methods for constructing a propositional formula over inequality constraints that is satisfied by the observations pertaining to the objects of a specific type, and falsified by the others. The formula then may serve as a classifier, as a compressed form of the data, and as an explicit representation of relationships inherent in the data. Opposed to many approaches in machine learning, the formula provides an explanation for the classifications obtained from it. On the other hand, the logical approach is sensitive to variations of the input data and relies on careful data cleaning. Technically, our algorithms take as input sets of positive and negative samples, T and F, where each sample is represented by an \(\ell \) -dimensional vector over a totally ordered domain of cardinality n. Our algorithms construct formulas with literals of the form \(x \ge d\) and \(x \le d\) that are satisfied by the samples in T and falsified by those in F. The running time is bounded by \(O(\left| T\right| n \ell ^2 \log ^2n + \left| T\right| \left| F\right| \ell ^3 \log ^2 n)\) . Our implementation in , publicly available from github, is able to derive formulas for many interesting instances within milliseconds.