Teaching

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After successful completion of this course, students will be able to:
• understand the formalisms for modelling, querying, and reasoning over knowledge graphs,
• apply the aforementioned formalisms to execute operations over knowledge graphs,
• create prototypes of queryable knowlege graphs using the techniques learned during the course,
• understand the role of knowledge graphs as a foundation to solve other problems in Artificial Intelligence,
• remember examples of real-world knowledge graphs and their applications in industry,
• communicate about the above aspects in English.

Knowledge Graphs (KG) allow for representing inter-connected facts or statements annotated with semantics. In KGs, concepts and entities are typically modeled as nodes while their connections are modeled as directed and labeled edges, creating a graph. In recent years, KGs have become core components of modern data ecosystems. KGs, as building blocks of many Artificial Intelligence approaches, allow for harnessing and uncovering patterns from the data.

In this lecture, students will learn about the foundations of modelling, querying, publishing, and reasoning over KGs.

Topics

1. Introduction to Knowledge Graphs
• AI and Knowledge: Representation and Reasoning
• Knowledge-Based Systems
• Knowledge Graphs
• Examples of Real-World Knowledge Graphs

2. The Resource Description Framework (RDF)
• Introduction to RDF
• RDF Serializations
• The RDF Vocabulary
• Operations over RDF Graphs: Isomorphism, Subgraph, Instance, Equivalence, Union, Merge

3. The SPARQL Query Language
• Structure of SPARQL Queries
• Basic Graph Patterns and Group Graph Patterns
• Filters, Functions, and Modifiers
• Querying Multiple (Named) RDF Graphs
• Querying RDF Graphs on the Web

4. Semantics of SPARQL
• SPARQL Query Processing
• SPARQL Algebra Expressions
• BGP Pattern Matching
• Evaluation of Algebra Expressions (eval function)
• SPARQL Set vs. Bag Semantics

5. Linked Data: Knowledge Graphs and Ontologies on the Web
• The Semantic Web and the Linked Data Principles
• Introduction to Vocabularies and Ontologies on the Web
• The RDF Schema (RDFS) Vocabulary
• Domain-specific Vocabularies and Ontologies on the Web

6. The Web Ontology Language (OWL)
• OWL Fragments
• OWL DL Axioms: Classes, Properties, and Individuals
• OWL DL Class and Property Construction
• OWL DL Inference: Consistency and Membership
• OWL for Data Integration

7. Entailment Regimes over Knowledge Graphs
• Model-theoretic Semantics
• Simple Interpretations
• D-Interpretations
• RDF Interpretations
• Overview of RDFS Interpretations

8. Reasoning over Knowledge Graphs
• Entailed Graphs
• Interpolation Lemma for Simple Interpretations
• D-inconsistencies
• SPARQL Query Processing with Reasoning

9. Quality in Knowledge Graphs
• Introduction to Data Quality
• The 5-star Linked Data Scheme
• Quality Constraints
• Specifying Constraints with the Shapes Constraints Language (SHACL)
• Data Constraints vs. Ontological Constraints
• SHACL Validation with Reasoning

10. Property Graphs
• Modelling Knowledge Graphs with Property Graphs
• Translations between and RDF and Property Graphs
• The Cypher Query Language

11. Knowledge Graph Embeddings
• Introduction to Representation Learning
• Negative Sampling
• Loss Functions
• Embeddings based on (Graph) Neural Networks
• Embeddings based on Translational Models
• Applications to Knowledge Graph Completion

12. Knowledge Graph Applications
• Knowledge Graphs in Enterprises
• Information Extraction from Non-semantic Sources
• Knowledge Graphs for Semantic Search
• Knowledge Graphs for Recommender Systems
• Knowledge Graphs for Question Answering Systems Knowledge Graphs and Large Language Models (LLMs)

Basic knowledge about the following topics is highly recommended but not mandatory: Graph theory, set theory, databases, logic.

The module consists of a lecture with accompanying exercise session, and exercise sheets. Selected topics will be complemented with hands-on sessions using Jupyter Notebooks (https://jupyter.org/) to show how KG technologies work in practice.

Written exam (90 minutes) in English.
The exam is designed to assess the student’s understanding of the theoretical foundations of knowledge graphs, including formalisms for modeling, querying, and reasoning, as well as real-world examples and applications.
The exam includes questions that evaluate comprehension and recall of fundamental concepts (e.g., define, explain, exemplify) and the ability to analyze and apply concepts (e.g, perform calculations).

• Aidan Hogan et al. Knowledge Graphs. 2020. https://arxiv.org/pdf/2003.02320.pdf
• Pascal Hitzler, Markus Krötzsch, Sebastian Rudolph. Foundations of Semantic Web Technologies. Chapman &
Hall/CRC, 2009.