We propose an adaption of the explanation-generating system LIME. While LIME relies on sparse linear models, we explore how richer explanations can be generated. As application domain we use images which consist of a coarse representation of ancient graves. The graves are divided into two classes and can be characterised by meaningful features and relations. This domain was generated in analogy to a classic concept acquisition domain researched in psychology. Like LIME, our approach draws samples around a simplified representation of the instance to be explained. The samples are labelled by a generator – simulating a black-box classifier trained on the images. In contrast to LIME, we feed this information to the ILP system Aleph. We customised Aleph’s evaluation function to take into account the similarity of instances. We applied our approach to generate explanations for different variants of the ancient graves domain. We show that our explanations can involve richer knowledge thereby going beyond the expressiveness of sparse linear models.