There is a fully funded PhD position available at the Institute of Neural Information Processing, Ulm University, Germany. At the institute we are interested in the mathematical foundations of intelligent behaviour in biological and artificial systems. The PhD topic will revolve around the fundamental question of how the abstraction capabilities of classic symbolic knowledge systems can be combined with the sub-symbolic pattern recognition capabilities of neural networks in order to allow neural networks to take existing knowledge into account when making predictions. The PhD position will be part of the newly established DFG graduate school KEMAI (Knowledge Infusion and Extraction for Explainable Medical AI). The structured PhD programme has a duration of 3 years with the possibility of extending for one more year. The candidate will have the opportunity both to make contributions to fundamental questions in AI and cognitive science and to apply their work directly in the context of medical imaging through collaboration with Ulm University Clinic. Within the same broad topic area there is a second PhD position available at the Institute of Medical Systems Biology that includes investigation of genetic markers.