Logical Analysis of Data (LAD) is a two-class learning algorithm which integrates principles of combinatorics, optimization, and the theory of Boolean functions. This paper proposes an algorithm based on mixed integer linear programming to extend the LAD methodology to solve multi-class classification problems, where One-vs-All (OvA) learning models are efficiently constructed to classify observations in predefined classes. The utility of the proposed approach is demonstrated through experiments on multi-class benchmark datasets.