Rule-Based Languages for Neurosymbolic AI

Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention. They complement the data-intensive statistical approaches of neural networks and language models with symbolic reasoning algorithms to function in high-stakes domains or in low-data regimes that characterize many real-world applications. We argue that the neurosymbolic combination of machine learning and formal reasoning is not a niche approach within AI, but rather includes many already successful techniques that are of crucial importance to the development of reliable, efficient and, ultimately, trustworthy systems. This perspective prompts a re-examination of the design of current AI systems. We show that many leading AI systems, including some that are not traditionally considered as neurosymbolic, can be analysed from the perspective of four principles of neurosymbolic AI design: Reasoning, Assurances, Interfacing and Learning (RAIL). Applying the RAIL framework offers a unified view of seemingly disparate AI systems, ranging from physics-aware machine learning to neuro-guided search (such as Google DeepMind's Alpha-* suite), causal learning and tool-augmented Large Language Models. Importantly, the RAIL principles will enable engineers to make better-informed and more principled decisions about the design and deployment of production-level AI systems. In this article, we introduce the RAIL principles, examine how they can be applied across major areas of AI, and illustrate how they may guide practitioners to integrate neurosymbolic methods into next-generation AI technologies.

Declarative logic programs offer a powerful and interpretable abstraction for encoding relational structure and neurosymbolic reasoning, by expressing dependencies as weighted compositional rules. However, inducing them from data remains fundamentally hard, bottlenecked by the combinatorial explosion of symbolic search spaces. LLMs have recently emerged as powerful hypothesis generators, but when used in isolation, they lack the capacity to do systematic inductive reasoning needed to reliably synthesize valid programs that fit complex relational distributions. We introduce grasp (Gradient-boosted Synthesis of Probabilistic logic programs), a neurosymbolic framework that casts relational structure learning as functional gradient boosting in which the weak learner is a first-order rule and the intractable inner search is delegated to an LLM proposal oracle. We evaluate grasp on four relational benchmarks spanning molecular toxicity prediction (Tox21), mutagenesis, and citation matching (Cora), and show that it improves over purely symbolic, neural, and LLM-based baselines, while producing interpretable weighted rule ensembles. By replacing combinatorial search with gradient-guided LLM hypothesis generation, grasp retains boosting guarantees without sacrificing the transparency of symbolic outputs.

Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI. While existing approaches extend the capabilities of ASP to real world domains, their reasoning pipelines depend on classical solvers, which is a bottleneck for scalability. To tackle this problem, we propose a new method to compute stable models, called decision-propagation (DProp), which alternates falsity decisions and truth propagations. Successful DProp computations are shown to capture the stable model semantics. We then develop Neural DProp (NDProp), a differentiable extension of DProp with neural computation for decisions and fuzzy evaluation for propagations. We evaluate the capabilities of NDProp for learning decision heuristics as well as neuro-symbolic integration, and compare it with existing neuro-symbolic approaches. The results show that NDProp can learn to efficiently compute stable models, and it improves accuracy and scalability on neuro-symbolic benchmarks.