Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning

TL;DR

The paper addresses the need for interpretable and accountable AI by surveying neural-symbolic computing as a principled framework that integrates robust neural learning with symbolic reasoning. It surveys three main representations for symbolic knowledge in neural nets—rule-based, formula-based, and embedding-based—and maps how these enable learning, reasoning, and knowledge extraction. It highlights key methodologies such as KBANN, CILP, LTNs, Tensorisation, DeepProbLog, and ILP hybrids, illustrating how perception and reasoning can be combined in both horizontal and vertical hybrids. The work provides a roadmap for building explainable AI systems that couple perception with structured knowledge, enabling principled, scalable reasoning and knowledge extraction across domains.

Abstract

Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns about interpretability and accountability of AI have been raised by influential thinkers. In spite of the recent impact of AI, several works have identified the need for principled knowledge representation and reasoning mechanisms integrated with deep learning-based systems to provide sound and explainable models for such systems. Neural-symbolic computing aims at integrating, as foreseen by Valiant, two most fundamental cognitive abilities: the ability to learn from the environment, and the ability to reason from what has been learned. Neural-symbolic computing has been an active topic of research for many years, reconciling the advantages of robust learning in neural networks and reasoning and interpretability of symbolic representation. In this paper, we survey recent accomplishments of neural-symbolic computing as a principled methodology for integrated machine learning and reasoning. We illustrate the effectiveness of the approach by outlining the main characteristics of the methodology: principled integration of neural learning with symbolic knowledge representation and reasoning allowing for the construction of explainable AI systems. The insights provided by neural-symbolic computing shed new light on the increasingly prominent need for interpretable and accountable AI systems.

Figures (4)

• Figure 1: Evolution of Reasoning and Learning in Time
• Figure 2: Knowledge representation of $\phi = \{ \mathrm{A} \leftarrow \mathrm{B} \wedge \mathrm{C} , \mathrm{B} \leftarrow \mathrm{C} \wedge \neg \mathrm{D} \wedge \mathrm{E} , \mathrm{D} \leftarrow \mathrm{E} \}$ using KBANN and CILP.
• Figure 3: Knowledge representation of $\phi = \{w: \mathrm{A} \leftarrow \mathrm{B} \wedge \mathrm{C} , w: \mathrm{B} \leftarrow \mathrm{C} \wedge \neg \mathrm{D} \wedge \mathrm{E} , w: \mathrm{D} \leftarrow \mathrm{E} \}$ using Penalty logic and Confidence rules
• Figure 4: Logic tensor network for $P(x,y) \rightarrow A(y)$ with $\mathcal{G}(x)= \mathbf{v}$ and $\mathcal{G}(y)= \mathbf{u}$; $\mathcal{G}$ are grounding (vector representation) for symbols in first-order language; and the tensor order in this example is $2$Serafini_2016.