Description Logic

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

• AKA: DL, Terminological System, Concept Language.
• Context:
  • It must contain a set of Unary Predicate Symbols, which are used to denote Concept Names.
  • It must contain a set of Binary Relations, which are used to denote Role Names.
  • It can contain Atomic Concepts and Atomic Roles.
  • It can define more complex Concept Terms and Role expressions by means of Recursion.
  • It can include Intensional Knowledge (T), by means of a set of Inclusion Assertions.
  • It can include Extensional Knowledge (A), by means of a set of Membership Assertions.
  • It can contain Constructors that allow the creation of new Terms using already defined Terms, to represent Complex Concepts and Roles.
  • It can be used by a DL-based Computing System.
  • It can be the focus of a Description Logics Discipline.
  • …
• Example(s):
  • OWL-DL and OWL-Lite.
  • EL++.
  • T={PERSON there exists a MALE FATHER; MALE in PERSON; FEMALE is in PERSON; FEMALE is not MALE}. A={MALE(Bob), PERSON(Mary), PERSON(Paul)}.
• See: Function-Free First-Order Logic, DL Rule, Web Ontology Language, Propositional Logic, First-Order Predicate Logic, Decision Problem.

---

---

References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/description_logic Retrieved:2016-1-9.
  • Description logics (DL) is a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order predicate logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems.

    DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as terminological knowledge). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language [OWL] and its profile is based on DLs. The most notable application of DLs and OWL is in biomedical informatics where DL assists in the codification of biomedical knowledge.

2011

• http://dl.kr.org/
  • The main effort of the research in knowledge representation is providing theories and systems for expressing structured knowledge and for accessing and reasoning with it in a principled way. Description Logics are considered the most important knowledge representation formalism unifying and giving a logical basis to the well known traditions of Frame-based systems, Semantic Networks and KL-ONE-like languages, Object-Oriented representations, Semantic data models, and Type systems.

2010

• Description Logics 2010, 23rd International Workshop on Description Logics

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Description_logic
  • 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.

2008

• (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3 doi:[http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3)
  • … Description Logics are useful and efficient at categorizing objects and creating a hierarchy of types. They can classify new concepts and specify constraints on the type hierarchy. But is this enough?
  • Using Conceptual Graphs to represent the underlying ontology, we have demonstrated a method for automated reasoning on ontologies. Type hierarchies and the canonical formation rules efficiently specialize graphs into concrete instances. A simple unification operation, using join and type subsumption, is used to perform knowledge conjunction of the concepts represented as graphs. The significance of our work is that the previously static knowledge representation of ontology is now a dynamic, functional reasoning system.
• (Oveisi, 2008) ⇒ Mehrdad Oveisi. (2008). “Belief Revision in Description Logics: A brief overview." Depth Exam Report. Simon Fraser University.
• TBD
  • DL axioms are statements that describe relations between class (property) descriptions characteristics of properties, such as asserting a

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

2007

• (Obitko, 2007) ⇒ Marek Obitko. (2007). “Translations between Ontologies in Multi-Agent Systems", Ph.D. dissertation, Faculty of Electrical Engineering, Czech Technical University in Prague. http://www.obitko.com/tutorials/ontologies-semantic-web/description-logics.html
  • Description logics (DL) are logics serving primarily for formal description of concepts and roles (relations). These logics were created from the attempts to formalize semantic networks and frame based systems. Semantically they are found on predicate logic, but their language is formed so that it would be enough for practical modeling purposes and also so that the logic would have good computational properties such as decidability. The focus of research in DLs is how the various DL constructs are usable for real world applications and what is the impact of them against the complexity of reasoning.

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.

2003

• (Baader et al., 2003) ⇒ Franz Baader (editor), Diego Calvanese (editor), Deborah McGuinness (editor), Daniele Nardi (editor), and Peter Patel-Schneider (editor). (2003). “The Description Logic Handbook”.

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

• (Borgida & Brachman, 2003) ⇒ Daniele Nardi, and Ronald J. Brachman. (2002). “An Introduction to Description Logics.” In: (Baader et al., 2003)
• (Borgida & Brachman, 2003) ⇒ Alex Borgida, and Ronald J. Brachman. (2002). “Conceptual Modelling with Description Logics.” In: (Baader et al., 2003)

2000

• (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 http://dl.kr.org/dl
  • 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.

---