The field of Neurosymbolic AI, also known as Neuro-Symbolic or Neural-Symbolic AI, aims to unite two disparate approaches to AI, symbolic reasoning and neural networks. Symbolic reasoning is often mathematically and logically explicit, and therefore suitable for formal deductive reasoning applications and knowledge representation. Neural or connectionist approaches such as Deep Learning, on the other hand, usually have inductive strategies, making them well suited for statistical and empirical tasks such as classification and prediction. Research on uniting both of these types of AI has led to many innovative techniques that extend the boundaries of both disciplines.

It is important to emphasize at the very beginning that Neurosymbolic AI is a young field, still actively being defined and explored. Many recent surveys such as [1, 2, 3] have sought to define the discipline but efforts are in many ways still scattered. To give an example, one of the challenges in this domain is that, due to the overwhelming conceptual difficulty of the task, it is never entirely clear a priori what a successful system should look like. Many adopt the techniques from neural networks to improve symbolic tasks, where statistics such as accuracy are very relevant for evaluating predictions and classifications. However, when we do the reverse and try to use symbolic systems to perform neural operations, these metrics are potentially redundant or meaningless, like asking how accurate a formal proof is. Considering this difference we can see quite clearly one of the largest distinguishing factors between different approaches to integration, namely: are we attempting to do symbolic reasoning with neural networks, performing neural network related tasks using symbols, using one type of AI to augment a task that is purely within the domain of the other, or some novel combination of the two? The answer to this question will guide how such a system is designed, developed, and evaluated, and how it could compare with others. In this book we will see examples of each of these approaches.

Broadly speaking, the hope of many of these efforts is to find some useful middle-ground between the rigid transparency of symbolic systems and more flexible yet highly opaque neural applications. Each strategy has clear advantages and disadvantages that would be useful occasionally to combine. Symbolic reasoning, for example, is usually entirely transparent and system behavior can be inspected at any level of execution. This useful characteristic is largely absent in neural systems, which often have a black-box style of unsupervised behavior. Yet the transparency comes at a cost. In order to achieve this interpretability, the symbolic systems must be manually written by human engineers, which is often extremely time consuming. If it were possible to somehow have both automated and trainable neural systems that can also justify their behavior in a way that can be interpreted by humans like a symbolic system, this would be in effect a best of both worlds scenario. This goal, along with many others in neurosymbolic reasoning, is of course a long ways off, but it is clear that advances in this direction would greatly serve the cause of AI in general.

This book is intended to follow and extend on the work in the previous book [4] which begun to lay out the current breadth of the field. The chapters in the current book are organized by theme, each chapter within the theme appearing in alphabetical order by surname of the first author. The first four chapters are overview or survey papers in the field, the following three discuss the fundamentals of neurosymbolic reasoning, following that are five chapters about neurosymbolic architectures, then we have four chapters about symbolic reasoning using Deep Learning, five about symbolic inference with Deep Learning, three chapters about improving Deep Learning with symbolic methods, four on explainable Deep Learning, and finally two chapters on natural language processing.

Chapters were all selected as invited contributions from an open call for abstract submissions that would combine previous works by authors. Papers were reviewed internally before publication. We thank all individuals who contributed to the publication of this book.

References

[1] Bader S, Hitzler P. Dimensions of neural-symbolic integration – A structured survey. In: Artëmov SN, Barringer H, d’Avila Garcez AS, et al., editors. We Will Show Them! Essays in Honour of Dov Gabbay, Volume One. College Publications; 2005. p. 167–194.

[2] Garcez Ad, Bader S, Bowman H, et al. Neural-symbolic learning and reasoning: a survey and interpretation. Neuro-Symbolic Artificial Intelligence: The State of the Art. 2022;342(1).

[3] Sarker MK, Zhou L, Eberhart A, et al. Neuro-symbolic artificial intelligence: Current trends. AI Communications. 2021;34(3):197–209.

[4] Hitzler P, Sarker MK, editors. Neuro-symbolic artificial intelligence: The state of the art. (Frontiers in Artificial Intelligence and Applications; Vol. 342). IOS Press; 2021. Available from: https://doi.org/10.3233/FAIA342.