Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks, yet they often struggle with spatial reasoning. This paper presents a novel neural-symbolic framework that enhances LLMs' spatial reasoning abilities through iterative feedback between LLMs and Answer Set Programming (ASP). We evaluate our approach on two benchmark datasets: StepGame and SparQA, implementing three distinct strategies: (1) direct prompting baseline, (2) Facts+Rules prompting, and (3) DSPy-based LLM+ASP pipeline with iterative refinement. Our experimental results demonstrate that the LLM+ASP pipeline significantly outperforms baseline methods, achieving an average 82% accuracy on StepGame and 69% on SparQA, marking improvements of 40-50% and 8-15% respectively over direct prompting. The success stems from three key innovations: (1) effective separation of semantic parsing and logical reasoning through a modular pipeline, (2) iterative feedback mechanism between LLMs and ASP solvers that improves program rate, and (3) robust error handling that addresses parsing, grounding, and solving failures. Additionally, we propose Facts+Rules as a lightweight alternative that achieves comparable performance on complex SparQA dataset, while reducing computational overhead.Our analysis across different LLM architectures (Deepseek, Llama3-70B, GPT-4.0 mini) demonstrates the framework's generalizability and provides insights into the trade-offs between implementation complexity and reasoning capability, contributing to the development of more interpretable and reliable AI systems.

We formalise some aspects of the neural-symbol design patterns of van Bekkum et al., such that we can formally define notions of refinement of patterns, as well as modular combination of larger patterns from smaller building blocks. These formal notions have been implemented in the heterogeneous tool set (Hets), such that patterns and refinements can be checked for well-formedness, and combinations can be computed.

Historically, the two encompassing streams of symbolic and sub-symbolic stances to AI evolved in a largely separate manner, with each camp focusing on selected narrow problems of their own. Originally, researchers favored the discrete, symbolic approaches towards AI, targeting problems ranging from knowledge representation, reasoning, and planning to automated theorem proving. While the particular techniques in symbolic AI varied greatly, the field was largely based on mathematical logic, which was seen as the proper ("neat") representation formalism for most of the underlying concepts of symbol manipulation. With this formalism in mind, people used to design large knowledge bases, expert and production rule systems, and specialized programming languages for AI. These symbolic logic representations have then also been commonly used in the machine learning (ML) sub-domain, particularly in the form of Inductive Logic Programming (discussed in the previous article), which introduced the powerful ability to incorporate background knowledge into learning models and algorithms. Amongst the main advantages of this logic-based approach towards ML have been the transparency to humans, deductive reasoning, inclusion of expert knowledge, and structured generalization from small data.

We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large neural models. The models are queried using a symbolic logic language. Interaction with the user then confirms or rejects a revision of the neural model using logic-based constraints that can be distilled into the model architecture. The approach is illustrated using the Logic Tensor Network framework alongside Concept Activation Vectors and applied to a Convolutional Neural Network.

Artificial intelligence (AI) researchers continue to face large challenges in their quest to develop truly intelligent systems. Topics of interest at the workshop include the representation of symbolic knowledge by connectionist systems; integrated neural-symbolic learning approaches; extraction of symbolic knowledge from trained neural networks; integrated neural-symbolic reasoning; biologically-inspired neural-symbolic integration; integration of logic and probabilities in neural networks; structured learning and relational learning in neural networks; applications in robotics, simulation, fraud prevention, semantic web, soware engineering, fault diagnosis, bioinformatics, visual intelligence, and so on.

Research on integrated neural-symbolic systems has made si gnificant progress in the recent past. In particular the understanding of ways t o deal with symbolic knowledge within connectionist systems (also cal led artificial neural networks) has reached a critical mass which enables the c ommunity to strive for applicable implementations and use cases. Recen t work has covered a great variety of logics used in artificial intelligenc e and provides a multitude of techniques for dealing with them within the con text of artificial neural networks. Already in the pioneering days of computational models of ne ural cognition, the question was raised how symbolic knowledge can be r epresented and dealt with within neural networks. The landmark paper [M cCulloch and Pitts, 1943] provides fundamental insights how propositional logic can be processed using simple artificial neural networks. Within the following decades, however, the topic did not receive much attention as research in artifi cial intelligence initially focused on purely symbolic approaches. The power of machine learning using artificial neural networking was not recogni zed until the 80s, when in particular the backpropagation algorithm [Rumelha rt et al., 1986] made connectionist learning feasible and applicable in pra ctice. These advances indicated a breakthrough in machine learnin g which quickly led to industrial-strength applications in areas s uch as image analysis, speech and pattern recognition, investment analysis, engine monitoring, fault diagnosis, etc. During a training process from raw dat a, artificial neural networks acquire expert knowledge about the problem dom ain, and the ability to generalize this knowledge to similar but previou sly unencountered situations in a way which often surpasses the abilities of hu man experts.