Link prediction on knowledge graphs is relevant to various applications, such as recommendation systems, question answering, and entity search. This task has been approached from different perspectives: symbolic methods leverage rule-based reasoning but struggle with scalability and noise, while knowledge graph embeddings (KGE) represent entities and relations in a continuous space, enabling scalability but often neglecting logical constraints from ontologies. Recently, neurosymbolic approaches have emerged to bridge this gap by integrating embedding-based learning with symbolic reasoning. This paper provides a structured review of state-of-the-art neurosymbolic methods for link prediction. Beyond a qualitative analysis, a key contribution of this work is a comprehensive experimental benchmarking, where we systematically compare these methods on the same datasets using the same metrics. This unified experimental setup allows for a fair assessment of their strengths and limitations, bringing elements of answers to following key questions: How accurate are these methods? How scalable are they? How beneficial are they for different levels of provided knowledge and to which extent are they robust to incorrect knowledge?

The goal of this thesis is to address knowledge graph completion tasks using neuro-symbolic methods. Neuro-symbolic methods allow the joint utilization of symbolic information defined as meta-rules in ontologies and knowledge graph embedding methods that represent entities and relations of the graph in a low-dimensional vector space. This approach has the potential to improve the resolution of knowledge graph completion tasks in terms of reliability, interpretability, data-efficiency and robustness.

Reproducibility is a desirable property of scientific research. On the one hand, it increases confidence in results. On the other hand, reproducible results can be extended on a solid basis. In rapidly developing fields such as machine learning, the latter is particularly important to ensure the reliability of research. In this paper, we present a systematic approach to reproducing (using the available implementation), replicating (using an alternative implementation) and reevaluating (using different datasets) state-of-the-art experiments. This approach enables the early detection and correction of deficiencies and thus the development of more robust and transparent machine learning methods. We detail the independent reproduction, replication, and reevaluation of the initially published experiments with a method that we want to extend. For each step, we identify issues and draw lessons learned. We further discuss solutions that have proven effective in overcoming the encountered problems. This work can serve as a guide for further reproducibility studies and generally improve reproducibility in machine learning.

Graph data is omnipresent and has a wide variety of applications, such as in natural science, social networks, or the semantic web. However, while being rich in information, graphs are often noisy and incomplete. As a result, graph completion tasks, such as node classification or link prediction, have gained attention. On one hand, neural methods, such as graph neural networks, have proven to be robust tools for learning rich representations of noisy graphs. On the other hand, symbolic methods enable exact reasoning on graphs. We propose Knowledge Enhanced Graph Neural Networks (KeGNN), a neuro-symbolic framework for graph completion that combines both paradigms as it allows for the integration of prior knowledge into a graph neural network model. Essentially, KeGNN consists of a graph neural network as a base upon which knowledge enhancement layers are stacked with the goal of refining predictions with respect to prior knowledge. We instantiate KeGNN in conjunction with two well-known graph neural networks, Graph Convolutional Networks and Graph Attention Networks, and evaluate KeGNN on multiple benchmark datasets for node classification.