This work proposes a hybrid approach to Data Augmentation that blends inductive and deductive reasoning. In particular, the approach effectively utilizes a modest collection of labeled images while employing logic programs to declaratively define the structure of new images, allowing for flexible and dynamic image generation; the use of logic programming ensures adherence to both domain-specific constraints and given desiderata. The resulting structures are then used for guiding the generation of new realistic images based on a dedicated Deep-Learning process. The general approach can be particularly of use in biomedical and healthcare scenarios, where building extensive datasets of quality images is in general a hard prerequisite for many applications that is challenging to meet. The approach is specialized to two real-world case studies featuring laryngeal endoscopic and cataract images, respectively, and experiments conducted for assessing the method are discussed.