Neuro-symbolic (NeSy) AI aims to develop deep neural networks whose predictions comply with prior knowledge encoding, e.g. safety or structural constraints. As such, it represents one of the most promising avenues for reliable and trustworthy AI. The core idea behind NeSy AI is to combine neural and symbolic steps: neural networks are typically responsible for mapping low-level inputs into high-level symbolic concepts, while symbolic reasoning infers predictions compatible with the extracted concepts and the prior knowledge. Despite their promise, it was recently shown that - whenever the concepts are not supervised directly - NeSy models can be affected by Reasoning Shortcuts (RSs). That is, they can achieve high label accuracy by grounding the concepts incorrectly. RSs can compromise the interpretability of the model's explanations, performance in out-of-distribution scenarios, and therefore reliability. At the same time, RSs are difficult to detect and prevent unless concept supervision is available, which is typically not the case. However, the literature on RSs is scattered, making it difficult for researchers and practitioners to understand and tackle this challenging problem. This overview addresses this issue by providing a gentle introduction to RSs, discussing their causes and consequences in intuitive terms. It also reviews and elucidates existing theoretical characterizations of this phenomenon. Finally, it details methods for dealing with RSs, including mitigation and awareness strategies, and maps their benefits and limitations. By reformulating advanced material in a digestible form, this overview aims to provide a unifying perspective on RSs to lower the bar to entry for tackling them. Ultimately, we hope this overview contributes to the development of reliable NeSy and trustworthy AI models.

Recent years have witnessed the rapid development of Neuro-Symbolic (NeSy) AI systems, which integrate symbolic reasoning into deep neural networks.However, most of the existing benchmarks for NeSy AI fail to provide long-horizon reasoning tasks with complex multi-agent interactions.Furthermore, they are usually constrained by fixed and simplistic logical rules over limited entities, making them far from real-world complexities.To address these crucial gaps, we introduce LogiCity, the first simulator based on customizable first-order logic (FOL) for an urban-like environment with multiple dynamic agents.LogiCity models diverse urban elements using semantic and spatial concepts, such as \texttt{IsAmbulance}(\texttt{X}) and \texttt{IsClose}(\texttt{X}, \texttt{Y}) . These concepts are used to define FOL rules that govern the behavior of various agents. Since the concepts and rules are abstractions, they can be universally applied to cities with any agent compositions, facilitating the instantiation of diverse scenarios.Besides, a key feature of LogiCity is its support for user-configurable abstractions, enabling customizable simulation complexities for logical reasoning.To explore various aspects of NeSy AI, LogiCity introduces two tasks, one features long-horizon sequential decision-making, and the other focuses on one-step visual reasoning, varying in difficulty and agent behaviors.Our extensive evaluation reveals the advantage of NeSy frameworks in abstract reasoning. Moreover, we highlight the significant challenges of handling more complex abstractions in long-horizon multi-agent scenarios or under high-dimensional, imbalanced data.With its flexible design, various features, and newly raised challenges, we believe LogiCity represents a pivotal step forward in advancing the next generation of NeSy AI.All the code and data are open-sourced at our website.

Over the last few decades, Artificial Intelligence (AI) scientists have been conducting investigations to attain human-level performance by a machine in accomplishing a cognitive task. Within machine learning, the ultimate aspiration is to attain Artificial General Intelligence (AGI) through a machine. This pursuit has led to the exploration of two distinct AI paradigms. Symbolic AI, also known as classical or GOFAI (Good Old-Fashioned AI) and Connectionist (Sub-symbolic) AI, represented by Neural Systems, are two mutually exclusive paradigms. Symbolic AI excels in reasoning, explainability, and knowledge representation but faces challenges in processing complex real-world data with noise. Conversely, deep learning (Black-Box systems) research breakthroughs in neural networks are notable, yet they lack reasoning and interpretability. Neuro-symbolic AI (NeSy), an emerging area of AI research, attempts to bridge this gap by integrating logical reasoning into neural networks, enabling them to learn and reason with symbolic representations. While a long path, this strategy has made significant progress towards achieving common sense reasoning by systems. This article conducts an extensive review of over 977 studies from prominent scientific databases (DBLP, ACL, IEEExplore, Scopus, PubMed, ICML, ICLR), thoroughly examining the multifaceted capabilities of Neuro-Symbolic AI, with a particular focus on its healthcare applications, particularly in drug discovery, and Protein engineering research. The survey addresses vital themes, including reasoning, explainability, integration strategies, 41 healthcare-related use cases, benchmarking, datasets, current approach limitations from both healthcare and broader perspectives, and proposed novel approaches for future experiments.

Background: The field of Artificial Intelligence has undergone cyclical periods of growth and decline, known as AI summers and winters. Currently, we are in the third AI summer, characterized by significant advancements and commercialization, particularly in the integration of Symbolic AI and Sub-Symbolic AI, leading to the emergence of Neuro-Symbolic AI. Methods: The review followed the PRISMA methodology, utilizing databases such as IEEE Explore, Google Scholar, arXiv, ACM, and SpringerLink. The inclusion criteria targeted peer-reviewed papers published between 2020 and 2024. Papers were screened for relevance to Neuro-Symbolic AI, with further inclusion based on the availability of associated codebases to ensure reproducibility. Results: From an initial pool of 1,428 papers, 167 met the inclusion criteria and were analyzed in detail. The majority of research efforts are concentrated in the areas of learning and inference (63%), logic and reasoning (35%), and knowledge representation (44%). Explainability and trustworthiness are less represented (28%), with Meta-Cognition being the least explored area (5%). The review identifies significant interdisciplinary opportunities, particularly in integrating explainability and trustworthiness with other research areas. Conclusion: Neuro-Symbolic AI research has seen rapid growth since 2020, with concentrated efforts in learning and inference. Significant gaps remain in explainability, trustworthiness, and Meta-Cognition. Addressing these gaps through interdisciplinary research will be crucial for advancing the field towards more intelligent, reliable, and context-aware AI systems.

Explainability is an essential reason limiting the application of neural networks in many vital fields. Although neuro-symbolic AI hopes to enhance the overall explainability by leveraging the transparency of symbolic learning, the results are less evident than imagined. This article proposes a classification for explainability by considering both model design and behavior of 191 studies from 2013, focusing on neuro-symbolic AI, hoping to inspire scholars who want to understand the explainability of neuro-symbolic AI. Precisely, we classify them into five categories by considering whether the form of bridging the representation differences is readable as their design factor, if there are representation differences between neural networks and symbolic logic learning, and whether a model decision or prediction process is understandable as their behavior factor: implicit intermediate representations and implicit prediction, partially explicit intermediate representations and partially explicit prediction, explicit intermediate representations or explicit prediction, explicit intermediate representation and explicit prediction, unified representation and explicit prediction. We also analyzed the research trends and three significant challenges: unified representations, explainability and transparency, and sufficient cooperation from neural networks and symbolic learning. Finally, we put forward suggestions for future research in three aspects: unified representations, enhancing model explainability, ethical considerations, and social impact.

Artificial Intelligence (AI) plays a significant role in enhancing the capabilities of defense systems, revolutionizing strategic decision-making, and shaping the future landscape of military operations. Neuro-Symbolic AI is an emerging approach that leverages and augments the strengths of neural networks and symbolic reasoning. These systems have the potential to be more impactful and flexible than traditional AI systems, making them well-suited for military applications. This paper comprehensively explores the diverse dimensions and capabilities of Neuro-Symbolic AI, aiming to shed light on its potential applications in military contexts. We investigate its capacity to improve decision-making, automate complex intelligence analysis, and strengthen autonomous systems. We further explore its potential to solve complex tasks in various domains, in addition to its applications in military contexts. Through this exploration, we address ethical, strategic, and technical considerations crucial to the development and deployment of Neuro-Symbolic AI in military and civilian applications. Contributing to the growing body of research, this study represents a comprehensive exploration of the extensive possibilities offered by Neuro-Symbolic AI.

A hallmark of intelligence is the ability to use a familiar domain to make inferences about a less familiar domain, known as analogical reasoning. In this article, we delve into the performance of Large Language Models (LLMs) in dealing with progressively complex analogies expressed in unstructured text. We discuss analogies at four distinct levels of complexity: lexical analogies, syntactic analogies, semantic analogies, and pragmatic analogies. As the analogies become more complex, they require increasingly extensive, diverse knowledge beyond the textual content, unlikely to be found in the lexical co-occurrence statistics that power LLMs. To address this, we discuss the necessity of employing Neuro-symbolic AI techniques that combine statistical and symbolic AI, informing the representation of unstructured text to highlight and augment relevant content, provide abstraction and guide the mapping process. Our knowledge-informed approach maintains the efficiency of LLMs while preserving the ability to explain analogies for pedagogical applications.

Neuro-Symbolic Artificial Intelligence (AI) is an emerging and quickly advancing field that combines the subsymbolic strengths of (deep) neural networks and explicit, symbolic knowledge contained in knowledge graphs to enhance explainability and safety in AI systems. This approach addresses a key criticism of current generation systems, namely their inability to generate human-understandable explanations for their outcomes and ensure safe behaviors, especially in scenarios with \textit{unknown unknowns} (e.g. cybersecurity, privacy). The integration of neural networks, which excel at exploring complex data spaces, and symbolic knowledge graphs, which represent domain knowledge, allows AI systems to reason, learn, and generalize in a manner understandable to experts. This article describes how applications in cybersecurity and privacy, two most demanding domains in terms of the need for AI to be explainable while being highly accurate in complex environments, can benefit from Neuro-Symbolic AI.

In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for machine learning researchers unaware of why the research community cares about relational representations, this article can serve as a gentle introduction. Second, for logical experts who are newcomers to the learning area, such an article can help in navigating the differences between finite vs infinite, and subjective probabilities vs random-world semantics. Finally, for researchers from statistical relational learning and neuro-symbolic AI, who are usually embedded in finite worlds with subjective probabilities, appreciating what infinite domains and random-world semantics brings to the table is of utmost theoretical import.

Artificial Intelligence plays a main role in supporting and improving smart manufacturing and Industry 4.0, by enabling the automation of different types of tasks manually performed by domain experts. In particular, assessing the compliance of a product with the relative schematic is a time-consuming and prone-to-error process. In this paper, we address this problem in a specific industrial scenario. In particular, we define a Neuro-Symbolic approach for automating the compliance verification of the electrical control panels. Our approach is based on the combination of Deep Learning techniques with Answer Set Programming (ASP), and allows for identifying possible anomalies and errors in the final product even when a very limited amount of training data is available. The experiments conducted on a real test case provided by an Italian Company operating in electrical control panel production demonstrate the effectiveness of the proposed approach.