An Introduction to Description Logic

Abstract

In this chapter, we introduce and explain the basic notions of Description Logic, including syntax, semantics and reasoning services, and we explain how the latter are used in applications. The concept language of the DL ALCIn this section, we will describe the central notions of Description Logic first on an intuitive level and then on a more precise level. As a running example, we use the domain of university courses and teaching, and we will use a conceptualisation given informally, in graphical form, in Figure 2.1. Please note that this is one way of viewing university teachingwhich might be very different from the reader's way of viewing it. Also, as it is an informal representation, different readers may interpret arrows in different ways; that is, our representation does not come with a well-defined semantics that would inform us in an unambiguous way how to interpret the different arrows. 1 In the next sections, we will describe our way of viewing university teaching in a DL knowledge base, thereby establishing some constraints on the meaning of terms like "Professor" and "teaches" used in Figure 2.1 and throughout this section.In Description Logic, we assume that we want to describe some abstraction of some domain of interest, and that this abstraction is populated by elements. 2 We use three main building blocks to describe these elements:• Concepts represent sets of elements and can be viewed as unary pred-1 Our graphical representation looks somewhat similar to an extended ER diagram, for which such a well-defined semantics has been specified [Che76, CLN94]. 2 We have chosen the term "elements" rather than "individuals" or "objects" to prevent the reader from making false assumptions.

When is Ontology-Mediated Querying Efficient?

“…Concepts and Ontologies. We introduce several widely used description logics, see [4] for more details. An ELI ⊥ -concept is formed according to the syntax rule C, D ::…”

“…where A, B, A 1 , A 2 range over concept names and r ranges over roles. It is well-known that every can be converted into normal form in linear time with the resulting ontology being equivalent up to the introduction of fresh concept names [4].…”

“…Adding the ontology serves the purpose of delivering more complete answers to queries and of enriching the vocabulary available for querying. Ontologies are often formulated in description logics (DLs), a family of ontology languages that has emerged from artificial intelligence, underlies the OWL 2 recommendation for ontology languages on the web, and whose members can be seen as decidable fragments of (two-variable guarded) first-order logic [4]. The actual queries in OMQs are typically conjunctive queries (CQs), unions of CQs (UCQs), or fragments thereof, query languages that are at the heart of relational databases [1].…”

Model Comparison Games for Horn Description Logics

“…As the data is typically much larger than both TBox and query, the appropriate efficiency measure for ontology-mediated query answering is data complexity, under which the database is the only input to the problem, while the TBox and query are regarded as fixed [3]. For ALC, deduction is EXPTIMEcomplete and ontology-mediated query answering with conjunctive queries is CONP-complete [2].…”

Extending the Description Logic ALC with More Expressive Cardinality Constraints on Concepts

“…4 Basically, given a set of concept descriptions M, the type of an individual in an interpretation consists of the elements of M to which the individual belongs. Such a type t can also be seen as a concept description C t , which is the conjunction of all the elements of t. We assume in the following, that M contains all subdescriptions of the concept descriptions occurring in E as well as the negations of these subdescriptions.…”