Bridging Logic Programming and Deep Learning for Explainability through ILP

This thesis proposes a hybrid approach that bridges Deep Learning (DL) and Logic Programming (LP) to produce accurate but also interpretable Artificial Intelligence (AI) systems. While neural networks achieve outstanding predictive accuracy, their opaque nature limits transparency and accountability. This lack of transparency hinders their adoption in domains that demand accountability and interpretability, such as medical applications. To address this issue, the general idea we propose is to use the predictions generated by DL models as input to an Inductive Logic Programming (ILP) task. The ILP component then learns logical rules that explain the model’s decisions in a form understandable to humans. In this framework, Deep Learning models, such as You Only Look Once (YOLO) for object detection, and Convolutional Neural Network (CNN) or Recurrent Neural Network (RNN) variants for classification and sequence tasks, are responsible for high-performance prediction, while ILP systems such as Inductive Learning of Answer Set Programs (ILASP) and Fast Learning of Answer Set Programs (FastLAS) are employed to extract symbolic rules. These systems induce sets of non-monotonic logical rules, expressed in Answer Set Programming (ASP), that capture relationships between input features and model predictions. The symbolic component enables the construction of interpretable explanations both in graphical form, via directed acyclic graphs generated by eXplainable Answer Set Programming (xASP), and textual form, facilitating translation into natural language. The framework is applied and evaluated in three different domains: i) short-term meteorological forecasting, focusing on rainfall and lightning prediction; ii) juridical reasoning, based on the logical representation of Italian Penal Code articles and Court of Cassation decisions; and iii) veterinary medicine, automating biological image analysis for bull spermatozoa classification and morphological assessment. In each case, the hybrid models demonstrate competitive predictive accuracy while producing concise and semantically meaningful explanations. We also compare our explanations with common post-hoc methods, such as Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP), and Large Language Model (LLM) outputs. Beyond the empirical evaluation, the thesis discusses several methodological challenges, including the scalability of ILP systems when applied to high-dimensional data. Overall, the research contributes a generalisable methodology for combining neural prediction with symbolic rule learning, offering a way towards interpretable, verifiable, and trustworthy AI. By demonstrating how ILP can formalise and explain complex neural reasoning processes, this work provides a step towards bridging data-driven learning with logic-based explanation.