SS 26

Welcome to the course Foundation of Neuro-Symbolic AI!

Modules content:
1. Logical Approaches [1]
- Semantics and syntax of Propositional Logic
- Logical inference algorithms
- Neural function decomposition and inference

2. Probabilistic Approaches [2]
- Independencies, Graphical Models and Sufficient Statistics
- Reasoning schemes and maximum likelihood estimation
- Causal models and inference

3. Statistical Models of Knowledge Graphs [3]
- Knowledge Graphs, Description Logic and Semantic Web Standards
- Query languages for inference
- Statistical Relational AI

4. Quantum Machine Learning [4]
- Circuit model of computation and measurement schemes
- Deutsch-Jozsa Algorithm and application in Neuro-Symbolic AI
- Quantum advantages in sampling and contractions

All concepts will be introduced in a unifying tensor network formalism [5], which will be developed sequentially during the course.
The topics are accompanied by demonstrations and exercises based on the python library tnreason.

Literature:
[1] Russell, Norvig: ArtificiaI Intelligence - A Modern Approach (fourth edition), Pearson Education 2021
[2] Koller, Friedman: Probabilistic Graphical Models: Principles and Techniques, MIT Press 2009
[3] Antoniou et al: A Semantic Web Primer (third edition), MIT Press 2012
[4] Schuld, Petruccione: Machine Learning with Quantum Computers (second edition), Springer 2021
[5] Goessmann: The Tensor-Network Approach to Efficient and Explainable AI, Technical Report on the ENEXA Project 2025