Description Logics

Description Logics (DLs) is a logic-based knowledge representation language. They are embodied in several knowledge-based systems and are used to develop various real-life applications.

DLs represent the knowledge of an application domain (the “world”) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individuals occurring in the domain (the world description).

DLs are equipped with a formal logic-based semantics, and use reasoning as a central service, allowing the inference of implicitly represented knowledge from the knowledge that is explicitly contained in a knowledge base.

DLs support the inference patterns of classification of concepts and classification of individuals.

• The classification of concepts determines subconcepts/superconcepts relationships, called subsumption relationships. It allows the deriving of conceptual structures - subsumption hierarchies. These hierarchies provide information about the relatedness between the concepts and help to speed-up the inferencing processes.
• The classification of individuals determines whether a given individual is always an instance of a certain concept. It provides information about the properties of the individual. Moreover, instance relationships are the ones that trigger the application of rules that insert additional facts into the knowledge base.

The reasoning procedures of DL are decision procedures that are aimed to always terminate. There is a trade-off between the expressive power of a given DL and its decidability. This trade-off is the subject of massive DL research.

DLs are derived from the “structured inheritance networks” [Brachman, 1977b; 1978], which were first realized in the system Kl-One [Brachman and Schmolze, 1985].

Sophisticated optimization techniques are used when implementing a system based on DL.

Basic Formalism

A knowledge representation system based on Description Logics provides facilities to set up knowledge bases, to reason about their content, and to manipulate them. A knowledge base (KB) comprises two components:

• the TBox
• the ABox

The TBox introduces the terminology, i.e., the vocabulary of an application domain, while the ABoxcontains assertions about named individuals in terms of this vocabulary.

The vocabulary consists of concepts, which denote sets of individuals, and roles, which denote binary relationships between individuals. In addition DL systems allow the building of complex descriptions of concepts and roles. The TBox is used to assign names to complex descriptions.

DLs have a model-theoretic semantics. Thus, statements in the TBox and in the ABox can be identified with formulae in first-order logic.

DLs have reasoning facilities too. Typical reasoning tasks for a terminology are to determine whether a description is satisfiable (i.e., non-contradictory), or whether one description is more general than another one, that is, whether the first subsumes the second. Also, it is important to find out in an ABox whether its set of assertions is consistent, that is, whether it has a model, and whether the assertions in the ABox entail that a particular individual is an instance of a given concept description.

Satisfiability checks of descriptions and consistency checks of sets of assertions help determining whether a knowledge base is meaningful at all. Subsumption tests help organizing the concepts of a terminology into a hierarchy according to their generality. A concept description can also be conceived as a query, describing a set of objects. Instance tests, help retrieving the individuals that satisfy the query.

References

Franz Baader, Werner Nutt - The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press New York, NY, USA, 2003.