The field of Robotics traditionally benefits from the progress achieved in the broader area of Artificial Intelligence (AI). The wave of popularity of modern data-driven systems is creating well-justified expectations that their application in Robotics will lead to even bigger advancements in the future. At the same time, the field is experiencing a paradigm shift towards robots that operate in open, unstructured everyday environments, tasked with activities that require commonsense skills and high-level cognition. Towards this direction, the CARAML project will conduct cutting-edge research in diverse subfields of AI at the intersection of Machine Learning models, especially neural ones, with symbolic methods, involving high-level abstractions and formal reasoning. This highly prominent emerging subfield of AI is becoming known as neuro-symbolic AI. Specifically, CARAML aims at basic research, with demonstrable results, in order to develop novel AI methods for one of the most fundamental problems in Robotics, that of object grasping, and in particular manipulationdriven robotic grasping of unknown household objects in clutter, taking into consideration human-robot symbiotic conditions. The problem challenges many aspects related to Robotics, from the need to coordinate low-level grasp with high-level task planning relying on imperfect perception, up to understanding not only the geometric, but also the semantic properties of previously unseen objects. The need to communicate the decision-making process in a human-understandable way is also critical.