From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey

TL;DR

The paper addresses the challenge of unifying learning and reasoning by comparing neurosymbolic AI (NeSy) and statistical relational AI (StarAI). It introduces seven cross-cutting dimensions to categorize and relate systems from both fields, covering inference style, logic syntax, semantics, learning scope, representations, integration paradigm, and applicable tasks. By surveying representative NeSy and StarAI approaches along these dimensions, the work highlights analogies and opportunities for cross-fertilization between probabilistic-logic and neural-symbolic paradigms. It also discusses open challenges in semantics, probabilistic reasoning, fuzzy semantics, structure learning, scalability, data efficiency, and symbolic representation learning, aiming to guide future integrated designs with practical impact.

Abstract

This survey explores the integration of learning and reasoning in two different fields of artificial intelligence: neurosymbolic and statistical relational artificial intelligence. Neurosymbolic artificial intelligence (NeSy) studies the integration of symbolic reasoning and neural networks, while statistical relational artificial intelligence (StarAI) focuses on integrating logic with probabilistic graphical models. This survey identifies seven shared dimensions between these two subfields of AI. These dimensions can be used to characterize different NeSy and StarAI systems. They are concerned with (1) the approach to logical inference, whether model or proof-based; (2) the syntax of the used logical theories; (3) the logical semantics of the systems and their extensions to facilitate learning; (4) the scope of learning, encompassing either parameter or structure learning; (5) the presence of symbolic and subsymbolic representations; (6) the degree to which systems capture the original logic, probabilistic, and neural paradigms; and (7) the classes of learning tasks the systems are applied to. By positioning various NeSy and StarAI systems along these dimensions and pointing out similarities and differences between them, this survey contributes fundamental concepts for understanding the integration of learning and reasoning.

Figures (5)

• Figure 1: The Bayesian network corresponding to the ProbLog program in Example \ref{['ex:problog']}
• Figure 2: The Markov Field corresponding to the Markov logic network in Example \ref{['ex:mln']}
• Figure 3: Knowledge-Based Artificial Neural Network. Network creation process. (1) the initial logic program; (2) the AND-OR tree for the query calls_mary; (3) mapping the tree into a neural network; (4) adding hidden neurons, (5) adding interlayer connections.
• Figure 4: dDNNF (left) and arithmetic circuit (right) corresponding to the ProbLog program in Example \ref{['ex:problog']}
• Figure 5: A neural reparametrization of the arithmetic circuit in Example \ref{['ex:kc']} as done by DeepProbLog (cf. Example \ref{['ex:deepproblog']}). Dashed lines indicate a negative output, i.e 1 - x. We use a different notation for negation than in Figure \ref{['fig:kc']} to stress that both leaves are parameterized by the same neural network.