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Description Logics

Aliases: Concept Languages, Terminological Systems

Keywords: abox, alc, dl, fact, logic, oil, oil+daml, ontology, owl, racer, riq, satisfiability, shiq, shoiq, subsumption, tbox

Categories: Natural Language

Author(s): Douglas Holmes

Description logics (DLs) are a group of knowledge representation methods which consist of a set of symbols and a collection of systematic rules governing their uses and relations to each other. DLs emphasise the use of distributing things into classes or categories (classification) and checking whether any of the formulae imply any other (subsumption reasoning). as their primary mode of drawing conclusions based on what is known (inference). For a variety of DLs, procedures which make decisions, tight complexity bounds, and algorithms which carry out useful inference (as well as their corresponding inference problems) are known. They are closely related to semantic networks and frames, from which they are descended, but come with a formal logic-based way of defining the relationships of characters or groups of characters to their meanings, (semantics), which their ancestors do not.

These semantics are defined by two basic notions. The first part being "concepts", which are unary predicates which represent sets of individuals and the second part being "roles", which are binary relations which represent pairs of individuals. What these individuals are is taken from the domain of the DL.

A specific DL is mainly characterised by the constructors it provides to form complex concepts and roles from formulae with no subformulaes (atomic fomulae. For example, Attributive Language with Complements (ALC) is comprised of two parts. Firstly, , the base language, facilitates i) negation of atomic concepts ii) expressing the intersection between concepts iii) and the use of universal and limited existential quantification. The second part is the extension permits complex concept negation i.e negation of concepts that are are comprised of other concepts.

AL can be extended in a number of other ways to increase expressive power, however, this leads to increased complexity, and the inherent difficulty in providing scalable algorithms for specific computational problems that entails.

The extensionality of DLs make them potentially highly expressive, which in conjunction with their inference services, make them suitable candidates for languages which have to exhaustivly and rigorously give conceptual sets of ideas about a domain (ontologies). The applications of ontologies extend to many fields of AI, such as Machine Learning and Natural Language, which means that "DLs" are pertinant to these fields as well.



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