Ramon Fernández Mir

Lauren Nicole DeLong, Ramon Fernández Mir, Jacques D. Fleuriot

Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and multi-relational data, methods for reasoning on graph structures have attempted to follow this neurosymbolic paradigm. Traditionally, such approaches have utilized either rule-based inference or generated representative numerical embeddings from which patterns could be extracted. However, several recent studies have attempted to bridge this dichotomy to generate models that facilitate interpretability, maintain competitive performance, and integrate expert knowledge. Therefore, we survey methods that perform neurosymbolic reasoning tasks on knowledge graphs and propose a novel taxonomy by which we can classify them. Specifically, we propose three major categories: (1) logically-informed embedding approaches, (2) embedding approaches with logical constraints, and (3) rule learning approaches. Alongside the taxonomy, we provide a tabular overview of the approaches and links to their source code, if available, for more direct comparison. Finally, we discuss the unique characteristics and limitations of these methods, then propose several prospective directions toward which this field of research could evolve.

Bartosz Piotrowski, Ramon Fernández Mir, Edward Ayers

We introduce a machine-learning-based tool for the Lean proof assistant that suggests relevant premises for theorems being proved by a user. The design principles for the tool are (1) tight integration with the proof assistant, (2) ease of use and installation, (3) a lightweight and fast approach. For this purpose, we designed a custom version of the random forest model, trained in an online fashion. It is implemented directly in Lean, which was possible thanks to the rich and efficient metaprogramming features of Lean 4. The random forest is trained on data extracted from mathlib -- Lean's mathematics library. We experiment with various options for producing training features and labels. The advice from a trained model is accessible to the user via the suggest_premises tactic which can be called in an editor while constructing a proof interactively.

Lauren Nicole DeLong, Ramon Fernández Mir, Zonglin Ji et al.

Biomedical datasets are often modeled as knowledge graphs (KGs) because they capture the multi-relational, heterogeneous, and dynamic natures of biomedical systems. KG completion (KGC), can, therefore, help researchers make predictions to inform tasks like drug repositioning. While previous approaches for KGC were either rule-based or embedding-based, hybrid approaches based on neurosymbolic artificial intelligence are becoming more popular. Many of these methods possess unique characteristics which make them even better suited toward biomedical challenges. Here, we survey such approaches with an emphasis on their utilities and prospective benefits for biomedicine.