Family of Logic Based KR Formalisms

Description Logics

• A Description Logic is characterized by a set of constructors that allow building complex descriptions or terms out of concepts and roles from atomic ones.
• Concepts correspond to classes and are interpreted as sets of objects.
• Roles correspond to relations and are interpreted as binary relations on objects.

Basic Concepts of DL

• Individuals are treated exactly the same as constants in FOL.
• Concepts are exactly the same as Unary Predicates in FOL.
• Roles are exactly the same as Binary Predicates in FOL.

Descriptions

• The basic unit of semantic significance is the Description.
• Description logics differ in the operators allowed.
• Descriptions can be used to define complex concepts, such as "HappyFather" as a man with both a son and daughter and all of whose children are either rich or happy.

Architecture

• Typical Architecture of DL consists of Knowledge Base, TBox, ABox, Inference System, and Interface.
• TBox contains definitions of terminology and assertions about individuals.
• ABox contains assertions about individuals.

Expressiveness

• The expressiveness of a description logic is determined by the operators that it uses.
• Adding or eliminating certain operators (e.g., ¬, ∪) increases or reduces the number of statements that can be expressed.
• Higher expressiveness implies higher complexity.

Description Logic Languages

• AL (Attributive Language) is the base and includes just a few operators.
• Other DLs are described by the additional operators they include.
• Examples of DL languages include ALC, KL-ONE, NIKL, KANDOR, BACK, CLASSIC, LOOM, FACT, RACER, DAML+OIL, OWL, Pellet, Jena, and FACT++.

Applications

• Description Logics are well-suited for the representation of and reasoning about ontologies, terminological knowledge, configurations, and configuration problems.
• They are also used in database schema design, evolution, and query optimization, and in source integration in heterogeneous databases/data warehouses.