Reasoning in Neurosymbolic AI

2025-05-22

AI Summary

Neural-symbolic AI urgently requires integrating formal reasoning with data-driven learning to address the limitations of large language models in data efficiency, fairness, and safety. This paper proposes an energy-based neural-symbolic system that establishes, for the first time, a formally verifiable correspondence between the energy minimization process of Restricted Boltzmann Machines (RBMs) and propositional logic inference—thereby unifying neural computation and symbolic reasoning. Methodologically, logical formulas are encoded as energy functions, and a joint neuro-symbolic training framework simultaneously optimizes knowledge representation and data fidelity. Experiments demonstrate: (1) empirical consistency between energy minimization and logical entailment; and (2) superior performance over purely symbolic, purely neural, and state-of-the-art neural-symbolic baselines on joint knowledge-and-data learning tasks. This work advances the paradigm of interpretable and accountable AI through principled integration of logic and learning.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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.

Problem

• Integrating reasoning and learning in neural networks for neurosymbolic AI
• Addressing data efficiency, fairness, and safety challenges in Large Language Models
• Using energy-based systems for logical reasoning and knowledge representation

Innovation

• Energy-based neurosymbolic AI system
• Combines learning and logical reasoning
• Uses Restricted Boltzmann Machines