# 4: Description Logics


A Description Logic (DL) is a structured fragment of FOL; more precisely: any (basic) Description Logic language is a subset of $$\mathcal{L}_{3}$$, i.e., the function-free FOL using only at most three variable names. Its representation is at the predicate level: no variables are present in the formalism. DLs provide a logical reconstruction and (claimed to be a) unifying formalism for other knowledge representation languages, such as frames-based systems, object-oriented modelling, Semantic data models, etc. They provide the language to formulate theories and systems declaratively expressing structured knowledge and for accessing it and reasoning with it, and they are used for, among others, terminologies and ontologies, logic-based conceptual data modelling, and information integration.

• 4.1: Prelude to Description Logics
• 4.2: Description Logics Primer
Description logics (DLs) are a family of knowledge representation languages that are widely used in ontology development. An important practical reason for this is that they provide one of the main underpinnings for the Web Ontology Language OWL as standardised by the World Wide Web Consortium (W3C). However, DLs have been used in knowledge representation long before the advent of ontologies in the context of the Semantic Web, tracing back to first DL modelling languages in the mid 1980s.
• 4.3: Important Description Logics
There are very many DLs, of which some are used more often than others. In this section, we will first look at ALC , for it is typically one of the languages used in DL courses, a basis to add various language features to, and it is much easier for showing how the principles of tableau work for DLs. Subsequently, we list the more expressive SROIQ , and finally comment on leaner fragments that are computationally better behaved.
• 4.4: Reasoning Services
The reasoning services for DLs can be divided into so-called ‘standard’ reasoning services and ‘non-standard’ reasoning services. In this section, only the standard ones are considered, because the ‘non-standard’ ones are typically focused on assisting modelers in the ontology authoring process, rather than purely deriving knowledge only.
• 4.5: Literature and Reference Material
• 4.E: Description Logics (Exercises)

This page titled 4: Description Logics is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Maria Keet.