Neural-Symbolic Learning and Reasoning: A Survey and Interpretation

TL;DR

The paper surveys neural-symbolic integration as a framework to co-design learning and reasoning by coupling symbolic logics with neural networks. It grounds theory in prolegomena, presents NSCA as a concrete implementation, and connects these ideas to cognitive science, neuroscience, and human-level AI. Technical sections detail fixed-point inference in networks, first-order logic embedding, and Markov logic, while other parts survey recent developments, multi-agent anchoring, and complexity considerations. The work highlights challenges in representation, learning-reasoning integration, and knowledge extraction, arguing for a multidisciplinary path toward robust, explainable, human-like cognition.

Abstract

The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.

Figures (6)

• Figure 1: General conceptual overview of a neural-symbolic system garcez_2009.
• Figure 2: A symmetric 3-order network, characterised by a 3-order energy function: $XYZ-3XY+2X+2Y$. Minima of this energy function are fixed points of the network. This network searches for satisfying solutions for the weighted conjunctive normal form (CNF): $(\neg X \vee \neg Y \vee Z) \wedge (X \vee Y)$. Note that the clauses of the weighted CNF are augmented by penalties reflecting the importance of each constraint.
• Figure 3: A Markov network with two constants Anna ($A$) and Bob ($B$).
• Figure 4: (a) Example SPNs implementing a junction tree with clusters $(X1 \text{ and } X2)$ and $(X1 \text{ and } X3)$ and separator $X1$. (b) Naive Bayes model with variables $X1$ and $X2$ and three components.
• Figure 5: Partial class definition for a relational sum-product network in a simple political domain.