Description Logic

Created on March 9, 2013, 1:20 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:31 p.m.

Description Logics (DLs) are a Family of Logics that are Fragments of First Order Logic. In general what one does in Description Logics is from simple Descriptions to create more complex Descriptions with the help of Constructors. The different Variants of Description Logics differ in the applied Constructors as there are Constructors with different Exprissivity. Originally these Description Logics have been developed from Semantic Networks. Description Logics have been developed to be decidable most times and some times they are also feasible which means that they do not have too high complexity.

The W3C standard for the Web Ontology Language is OWL version 1 is based on SHROID and OWL version 2 is based on the SHORIQ(D) Descriptions Logics.

  • DLs are Fragments of FOL
  • In DL from simple Descriptions more complex descriptions are created with the Help of Constructors.
  • DLs differ in applied Constructors (Expressivity)
  • DLs have been developed from "Semantic Networks"
  • DLs are decideable (most times)
  • DLs posses sufficient Expressivity (most times)
  • DLs are related to Modal Logics

  • e.g. W3C Standard OWL 2 DL is based on Description Logics


The Web Ontology Language considers more complex Description Logics that go beyond ALC. If all the roles that are considered in ALC are transitive, then the Letter ALC changes to S. Datatypes are for example Strings or Integers.

The Constructors form and build up single Languages in Description Logics.

Number Restriction

Number restrictions restrict the number of Individuals that are related by a Role. For example, Quartet is always four. Thus, one has greate than and less than as well as equal.

There are also qualified number Restriction. For instance a String Quartet would be for Persons that all play String. Therefore a qualified number restriction has alos a Class Restriction on the Range of that Role or Property.

Set of Individuals

Set of Individuals are closed Sets or Classes, which are also called Nominals, line up or enumerate Class Members. Classes are defined by enumeration by its Members.

Role Hierarchy

Role Hierarchies are given by subclass relations.

Inverse Roles

In Inverse Roles one takes Domain and Range vice versa and exchanges Domain and Range.


Tags: description, decidable, constructors
Categories: Concept
Parent: Description Logics

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