Design research programs attempt to bring together the properties of available materials and the demands derived from intended applications. The logic of problem states and state transitions in such programs, including assessment criteria and heuristic principles, is described in settheoretic terms, starting with a naive model comprising an intended profile and the operational profile of a prototype. In a first concretization the useful distinction between structural and functional properties is built into the model. In two further concretizations the inclusion of potential applications is motivated and described for the case of drug research as well as the inclusion of potential realizations for the case of complex products. Next, another line of concretization of the naive model, the incorporation of potentially relevant properties, is sketched. Then the partial analogy between “product-” and “truth-approximation” is indicated. We conclude with some remarks about the usefulness of our models for products reaching the market in comparison to the the so-called social construction of technology approach.