Semantic Web Technologies – Ontology and logic

Summary of week three for the course Knowledge Engineering with Semantic Web Technologies 2015 by Harald Sack at OpenHPI.

This lecture deals with ontologies. If you want to speak a common language, you need:

  • common symbols and concepts (Syntax)
  • agreement about their meaning (Semantics)
  • classification of concepts (Taxonomy)
  • associations and relations of concepts (Thesauri)
  • rules and knowledge about which relations are allowed and make sense (Ontologies) (Dr. Harald Sack: Knowledge Engineering with Semantic Web Technologies presentation slides; Lecture 3: Ontologies and Logic 3.1 Ontologies Basics, Autumn 2015)

We define knowledge as a subset of true beliefs. A formal representation of this are ontologies. In philosophy it is also defined as the study of the nature of being and existence and basic categories for beings. In Computer Science: An Ontology is an explicit formal specification of a shared conceptualization (Thomas Gruber – A Translation Approach to Portable Ontology Specifications) Its principles are:

  • concept: model of the world
  • explicit: must be specified
  • formal: must be machine-readable
  • shared: all must understand it the same way

You can divide ontologies by two ways:

  • On their level of generality (top level ontologies that categorize everything in the world (example by John F. Sowa)), or specific for a model, a task or an application
  • On their level of expressivity (how much can you get out of an ontology?)
  • The next thing we need is formal logic. We need formal logic because with formal logic we can deduce things automatically which we cannot do using informal logic. We need propositional logic (make propositions based on true/false values)and first order logic to do this. For a formula the following terms are defined:
  • tautological: all interpretations are true
  • satisfyable: if a model exists for the formula
  • refutable: if exists an interpretation which is not a model
  • unsatisfiable: if no model exists

The next lecture was the tableaux algorithm. This one is used for automated reasoning. You basically create a decision tree and proof by refusion. Lecture 8 deals with description logic. It is important to know that there are several description logics out there. We do not use first order logic to build our ontologies because it would be too bulky. Part 9 deals with different assumptions for the logic:

  • No Unique name Assumption: in description logic individuals can have more than one name, therefore you have to specify that.
  • Open World Assumption: in an empty ontology, everything is possible. You define only what is forbidden.<> Closed World Assumption: Everything that cannot be shown to be true is false, so you have to define everything while creating it –> Databases.


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