Description Logic

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A Description Logic is a logic system designed to represent concepts and relations.






  • (Wikipedia, 2009) ⇒
    • Description logics (DL) are a family of formal knowledge representation languages. They are more expressive than propositional logic but have more efficient decision problems than first-order predicate logic.
    • DLs are used in Artificial Intelligence for formal reasoning on the concepts of an application domain (known as terminological knowledge). They are of particular importance in providing a logical formalism for Ontologies and the Semantic Web. The most notable application outside information science is in bioinformatics where DLs assist in the codification of medical knowledge.
    • The name description logic refers, on the one hand, to concept descriptions used to describe a domain and, on the other hand, to the logic-based semantics which can be given by a translation into first-order predicate logic. Description logic was designed as an extension to frames and semantic networks, which were not equipped with formal logic-based semantics. They form a middle ground solution: including some more expressive operations than propositional logic and having decidable or more efficient decision problems than first order predicate logic. Description logic was given its current name in the 1980s. Previous to this it was called (chronologically): terminological systems, and concept languages. Today description logic has become a cornerstone of the Semantic Web for its use in the design of ontologies. The OWL-DL and OWL-Lite sub-languages of the W3C-endorsed Web Ontology Language (OWL) are based on a description logic.
    • Syntax of description logics consists of
      • A set of unary predicate symbols that are used to denote concept names;
      • A set of binary relations that are used to denote role names;
      • A recursive definition for defining concept terms from concept names and role names using constructors.
    • In general, a concept denotes the set of individuals that belongs to it, and a role denotes a relationship between concepts.


property is transitive instanceOf relations between (pairs of) individuals and classes (properties).


Knowledge representation system based on DLs consists of two components - TBox and ABox. The TBox describes terminology, i.e., the ontology in the form of concepts and roles definitions, while the ABox contains assertions about individuals using the terms from the ontology. Concepts describe sets of individuals, roles describe relations between individuals.


theory, implementation, and applications]." Cambridge University Press. ISBN:0521781760


  • (Lambrix, 2000) ⇒ Patrick Lambrix. (2000). “Part-Whole Reasoning in an Object-Centered Framework." Lecture Notes in Computer Science. Springer.
    • QUOTE: Description logics are languages tailored for expressing knowledge about concepts and concept hierarchies. The concept hierarchies represent the isa relation between concepts. Description logics are usually given a Tarskistyle declarative semantics, which allows them to be seen as sub-languages of predicate logic. The main entities in description logics are:
      • concepts, which can be considered as unary predicates which are interpreted as sets of objects over a domain. Examples of concepts are soccer-team and ida-employee.
      • roles which can be considered as binary predicates which are interpreted as binary relations between the objects in the domain. An example of a role is member which may represent a relation between a team and the persons belonging to the team.
      • individuals which are interpreted as objects in the domain. For example, a particular member of a team would be represented by an individual.
    • Footnote: Description logics have also been referred to as terminological logics, concept languages and KL-ONE-like languages. They have their origin in semantic networks and frame-based systems. The web page of the description logic community is found at address
    • In description logics the distinction between terminological knowledge and assertional knowledge is often made. The terminological knowledge includes knowledge about concepts while the assertional knowledge includes knowledge about individuals. In this section we de ne a language for the representation of terminological knowledge while in the next section we de ne a language for the representation of assertional knowledge.

      Assertional statements are used to make statements about individuals. An assertional statement is of the form i :: C, where i is an individual name (<symbol>) and C a concept description (<concept-descr>) as de ned before. This means then that "[i] 2 "[C]. The information that is explicitly stated in an assertional statement is said to be told information. An Abox is a nite set of assertional statements. We say that an individual is de ned in an Abox if it appears in any one of the statements in the Abox. We assume that within one Abox an individual has a unique name.