The paper describes a new, logic-based methodology for analyzing observations. The key features of the Logical Analysis of Data (LAD) are the discovery of minimal sets of features necessary for explaining all observations, and the detection of hidden patterns in the data capable of distinguishing observations describing ``positive'' outcome events from ``negative'' outcome events. Combinations of such patterns are used for developing general classification procedures. An implementation of this methodology is described in the paper along with the results of numerical experiments demonstrating the classification performance of LAD in comparison with the reported results of other procedures. In the final section we describe three pilot studies on applications of LAD to oil exploration, psychometric testing, and the analysis of developments in the Chinese transitional economy. These pilot studies demonstrate not only the classification power of LAD, but also its flexibility and capability to provide solutions to various case-dependent problems.