Neural-symbolic (NeSy) AI has gained a lot of popularity by enhancing learning models with explicit reasoning capabilities. Both new systems and new benchmarks are constantly introduced and used to evaluate learning and reasoning skills. The large variety of systems and benchmarks, however, makes it difficult to establish a fair comparison among the various frameworks, let alone a unifying set of benchmarking criteria. This paper analyzes the state-of-the-art in benchmarking NeSy systems, studies its limitations, and proposes ways to overcome them. We categorize popular neural-symbolic frameworks into three groups: model-theoretic, proof-theoretic fuzzy, and proof-theoretic probabilistic systems. We show how these three categories have distinct strengths and weaknesses, and how this is reflected in the type of tasks and benchmarks to which they are applied.

This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proof-based; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.