Foundations of AI IV
Foundations of Artificial Intelligence IV

Knowledge representation

Start date
November 2021
4 weeks à 3 hours


The course "Foundations of Artificial Intelligence IV" introduces into the representation of conceptual knowledge using ontologies. The course explains the theoretical foundations of modern ontological languages such as OWL that are based on description logics developed within AI.

The first module introduces into the foundations of conceptual knowledge representation.

The first part discusses different types of knowledge and motivates the need to represent conceptual knowledge in an AI system. The module touches upon the history of knowledge representation in AI and its roots in philosophical logic. It summarizes early attempts of AI researchers to represent conceptual knowledge in frames and semantic nets.

The second part explores the foundations of knowledge representation systems using mathematical logic. It introduces the basic ideas behind description logic systems and the separation of abstract conceptual knowledge in the form of terminological descriptions in the so-called TBox from knowledge about concrete individuals in the form of assertions in the ABox is introduced. The need for sound, complete, and decidable algorithms that an AI system can use to reason with conceptual knowledge and the limits posed by mathematical logic are discussed.

The third part introduces the description logic ALC and defines its syntax and semantics. The relationship of ALC with first-order predicate logic is explored and limitations in the expressivity of ALC are discussed. Examples illustrate how conceptual knowledge is represented using an ALC TBox and ABox.

The fourth part dives deeper into the reasoning services offered by a description logic system and explores in detail how TBox and ABox knowledge is used to derive implicit knowledge. Reasoning services such as for example subsumption, classification, and realization are defined and illustrated with the help of examples.

The second module gives an overview of web ontologies and the semantic web.

The first part explains how ontologies and knowledge graphs are represented today using standards such as RDF, RDF Schema, and ontology web language OWL as a foundation of the semantic web. The syntax of OWL is defined. Its semantics is clear from the discussion of the ALC description logic. Practical applications today do not reason over ontologies, but query the information stored in these ontologies. The part therefore concludes with an overview over the ontology query language SPARQL.

The second part discusses unsolved problems in knowledge representation and motivates the need for non-monotonic reasoning and dealing with exceptions in the knowledge base of an AI system.


The course is based on the textbook by Stuart Russell and Peter Norvig: Introduction to Artificial Intelligence, 3rd edition, 2012 or 4th edition, 2020. The 3rd edition is also available in German: Stuart Russell und Peter Norvig: Künstliche Intelligenz - Ein Moderner Ansatz, 3. aktualisierte Auflage, Pearson 2012. The course also uses additional material from the books: R. Brachman, H. Levesque: Knowledge Representation & Reasoning, Morgan Kaufmann, 2004 and F. Baader, D. Calvanese, D. McGuinness, D. Nardi, P. Patel-Schneider: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, 2nd edition, 2007.

The course is held in English language with German subtitles.



This course is part of the course series "Foundations of Artificial Intelligence I-V":

  • Foundations of Artificial Intelligence I: Introduction to AI, Agents
  • Foundations of Artificial Intelligence II: Search algorithms
  • Foundations of Artificial Intelligence III: Logic and satisfiability
  • Foundations of Artificial Intelligence IV: Knowledge representation
  • Foundations of Artificial Intelligence V: Constraint solving problems

The single courses deal with different methodological complexes of AI. 

Which topics will be covered?

Module Representation of Conceptual Knowledge

  • Introduction
    • Types of knowledge
    • Ontologies and taxonomies
    • Frames and semantic nets
  • Description logic systems
    • Relation with first-order predicate logic
    • TBox and ABox representations
  • Description logic ALC
    • Syntax and Semantics
    • Complex concept descriptions
    • Interpretation of concepts and roles
    • Expressivity and decidability
  • Reasoning services in description logics
    • General concept inclusion and subsumption
    • Combined TBox/ABox reasoning
    • Reasoning as satisfiability checking
    • Reasoning with structural rules


Module Web ontologies and the Semantic Web

  • Introduction to the Semantic Web
    • The vision and architecture of the semantic web
    • RDF and RDF Schema
    • The Ontology web language family OWL
    • The Ontology editor Protegé
  • Querying the semantic web with SPARQL
    • Subgraph Matching
    • Query Pattern
    • Query Federation



Module Challenges in Knowledge Representation

  • The Frame problem in AI
  • Non-monotonic reasoning and belief revision
  • Dealing with exceptions and default assumptions in knowledge bases
  • Open research problems in knowledge representation


What will I achieve?

By the end of the course, you‘ll be able to

  • distinguish different types of knowledge,
  • understand the foundations of conceptual knowledge representation, the semantic web and knowledge graphs,
  • discuss reasoning services needed to derive implicit knowledge,
  • understand the basics of the ontology query language SPARQL,
  • assess limitations of currently ontology representations when dealing with exceptions and non-monotonic revisions.


Which prerequisites do I need to fulfill?

A solid understanding of first-order predicate logic is required to fully understand the theoretical material presented in this course. The course III in this course series on Logic and Satisfiability provides these foundations. Participants, who are mostly interested in learning about the basics of ontologies and for what they can be used in practice, can follow the main ideas presented in this course and are recommended to concentrate on the practical illustrating examples.

Who is offering this course?

Jana Koehler
Prof. Dr. Jana Koehler
Deutsches Forschungszentrum für Künstliche Intelligenz
Universität des Saarlandes
Artificial Intelligence Group / Saarland University
Tobias Bleymehl
Tobias Bleymehl
Artificial Intelligence Group / Saarland University
Annika Engel
Annika Engel
Deutsches Forschungszentrum für Künstliche Intelligenz
Andrea Nawrath-Herz
Andrea Nawrath-Herz
Deutsches Forschungszentrum für Künstliche Intelligenz

What else should I know?

Learning format:
Online course
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