Abstract. The work reported in this article continues investigations in a theoretical framework for Concept Theories based on mathematical logic. The general idea is that the intension of a concept is defined by some equivalence class of theories, whereas the extension is given by the models of the theory. The fact that extensions depend on structures that are necessary to interpret the formulae of the logic, already provides an argument to put more emphasis on the intension. Starting from the simple Ganter-Wille theory of formal concept analysis first-order theories that are interpreted in a fixed structure or in more than one structure are introduced. The Ganter-Wille Concept Theory turns out.
