Reasoning in Neurosymbolic AI

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the area of neurosymbolic Artificial Intelligence (AI). In this chapter, a simple energy-based neurosymbolic AI system is described that can represent and reason formally about any propositional logic formula. This creates a powerful combination of learning from data and knowledge and logical reasoning. We start by positioning neurosymbolic AI in the context of the current AI landscape that is unsurprisingly dominated by Large Language Models (LLMs). We identify important challenges of data efficiency, fairness and safety of LLMs that might be addressed by neurosymbolic reasoning systems with formal reasoning capabilities. We then discuss the representation of logic by the specific energy-based system, including illustrative examples and empirical evaluation of the correspondence between logical reasoning and energy minimization using Restricted Boltzmann Machines (RBM). Learning from data and knowledge is also evaluated empirically and compared with a symbolic, neural and a neurosymbolic system. Results reported in this chapter in an accessible way are expected to reignite the research on the use of neural networks as massively-parallel models for logical reasoning and promote the principled integration of reasoning and learning in deep networks. We conclude the chapter with a discussion of the importance of positioning neurosymbolic AI within a broader framework of formal reasoning and accountability in AI, discussing the challenges for neurosynbolic AI to tackle the various known problems of reliability of deep learning.