Neuro-Symbolic Artificial Intelligence

Goal

The course introduces the fundamental principles and methods of Neuro-Symbolic Artificial Intelligence, namely the integration of neural machine learning with knowledge representation and logical reasoning, with the aim of developing “hybrid” models that combine the advantages of these two foundational branches of AI and overcome their respective limitations.

The course covers the methodological foundations and design patterns of neuro-symbolic AI, including different types of neuro-symbolic architectures and approaches for combining and integrating learning and reasoning. It then focuses on applications of neuro-symbolic AI in temporally evolving environments, characterized by streams of multimodal data, the occurrence of complex and critical events or states, and interactions among multiple agents.

By the end of the course, students are expected to be familiar with methods that combine neural learning with prior or discovered knowledge, with the aim of developing reliable models for understanding and forecasting the evolution of dynamic domains, as well as for designing trustworthy multi-agent AI systems that act on the basis of perception, reasoning, and situational awareness.

Upon successful completion of the course, students will be able to:

• Understand the motivations and fundamental principles of neuro-symbolic AI.

• Distinguish the main categories of neuro-symbolic architectures and assess their advantages and limitations.

• Understand the basic mechanisms of differentiable logical and probabilistic reasoning, and their use as a foundation for developing integrated neuro-symbolic systems.

• Implement neuro-symbolic systems in which symbolic knowledge and logical constraints can guide learning.

• Understand the principles of complex event recognition and forecasting in dynamic, multimodal, and multi-agent environments.

• Be familiar with applications of neuro-symbolic AI in high-criticality domains that require trustworthy AI systems, such as the monitoring and management of critical infrastructures, dynamic biomedical applications, autonomous systems, and related areas.

• Formulate and evaluate ways in which the integration of learning and formal reasoning can contribute to the development of trustworthy solutions for emerging frontier technologies, such as generative and agentic AI.

Contents

Lecture 1: Introduction to neuro-symbolic AI and the technical aspects of trustworthy AI. Interpretability, robustness, uncertainty management, and out-of-distribution generalization. Presentation of representative applications of neuro-symbolic AI in perception, temporal reasoning, event recognition and forecasting, situational awareness, and agentic systems. Overview of the structure and thematic axes of the course.

Lecture 2: Differentiable logical reasoning I. Fuzzy operators and examples of fuzzy neuro-symbolic systems. Introduction to probabilistic logical reasoning and probabilistic graphical models.

Lecture 3: Differentiable logical reasoning II. Theoretical foundations of probabilistic logical reasoning, Weighted Model Counting, Knowledge Compilation, and differentiable circuits. Trainable logical architectures and representative implementations.

Lecture 4: Study of neuro-symbolic architectures and design patterns. Architectures for logical reasoning over sensory data. Architectures for imposing constraints on the behavior of neural networks. Semantic loss functions and training under indirect supervision through symbolic knowledge. Reasoning shortcuts and mitigation strategies.

Lecture 5: Introduction to complex event recognition from data streams. Basic concepts: primitive and complex events, temporal constraints, event composition, and the extraction of high-level states from streams of low-level observations. Overview of applications in critical infrastructure surveillance, maritime situational awareness, biomedical monitoring, and related areas. Symbolic approaches to complex event recognition. Temporal logics and efficient temporal reasoning techniques with correctness guarantees.

Lecture 6: Probabilistic approaches to complex event recognition. Probabilistic temporal logics applied to multimodal data streams. Performance analysis with respect to the correctness and complexity of event recognition.

Lecture 7: Neuro-symbolic techniques for complex event recognition. Probabilistic temporal logic with algebraic operations. Differentiable probabilistic logic. Techniques for improving computational complexity.

Lecture 8: Introduction to sequence modelling and forecasting future behavior. Fundamentals of probabilistic sequence modelling, Markov chains and Markov models, and finite-state automata as interpretable sequence models and as patterns of complex events.

Lecture 9: Complex event forecasting in data streams, as an application of sequence modelling. Overview of neural, statistical, symbolic, and neuro-symbolic techniques. The role of early event and state forecasting in decision-making.

Lecture 10: Translation of temporal logics into finite-state automata and differentiable temporal reasoning. Neuro-symbolic techniques for learning logical structure from multimodal temporal data. Introduction to learning world models and to the use of neuro-symbolic variants of such models for efficient, controllable, and trustworthy decision-making.

Lecture 11: Representative research topics and overview of frontier research directions in neuro-symbolic AI.

Bibliography

• Hitzler, P., & Sarker, M. K. (Eds.). Neuro-Symbolic Artificial Intelligence: The State of the Art. IOS Press, 2022.

• Marra, G., Dumančić, S., Manhaeve, R., & De Raedt, L. “From Statistical Relational to Neurosymbolic Artificial Intelligence: A Survey.” Artificial Intelligence, 2024.

• Shakarian, P., Baral, C., Simari, G. I., Xi, B., & Pokala, L. Neuro-Symbolic Reasoning and Learning. Springer, 2023.

• Barber, D. Bayesian Reasoning and Machine Learning. Cambridge University Press, 2012.

• Wooldridge, M. An Introduction to MultiAgent Systems. John Wiley & Sons, 2009.

• Hopcroft, J. E., Motwani, R., & Ullman, J. D. Introduction to Automata Theory, Languages, and Computation. 3rd edition, Addison-Wesley, 2007.

• Darwiche, A., & Marquis, P. “A Knowledge Compilation Map.” Journal of Artificial Intelligence Research, 17, 229–264, 2002.

• Gallager, R. G. Stochastic Processes: Theory for Applications. Cambridge University Press, 2013.

• Hyndman, R. J., & Athanasopoulos, G. Forecasting: Principles and Practice. OTexts, 2018.

• Giatrakos, N., et al. “Complex Event Recognition in the Big Data Era: A Survey.” The VLDB Journal, 29(1), 313–352, 2020.

• Selected research articles related to the lectures.

Related MSc Courses

• University of California, Berkeley: Neurosymbolic AI

• Carnegie Mellon University: Neuro-Symbolic AI

• TU Wien, Master in Logic and Artificial Intelligence: Neurosymbolic Reasoning module

• University of Liverpool: Neuro-Symbolic AI and Knowledge Engineering

• Chalmers University of Technology, Sweden: Neuro-Symbolic AI