Family of Logic Based KR Formalisms

What are the main components described in the family of logic-based KR formalisms?

What distinguishes the family of logic-based KR formalisms?

Who led the major focus of KR research in the 80s?

List three major systems and languages used in the 80s for Description Logics.

Name two Semantic web languages that are based on Description Logics.

What are Description Logics well-suited for representing and reasoning about?

What is the difference between primitive concepts and defined concepts in Description Logic?

How are individuals, concepts, and roles treated in Description Logic?

What is the basic unit of semantic significance in Description Logic?

How is a 'happy father' described in Description Logic if it is defined as a man with both a son and daughter, and all of whose children are either rich or happy?

What are TBox and ABox in the context of Description Logic?

How does the expressiveness of a description logic impact the complexity of the system?

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.

Explore the family of logic-based knowledge representation formalisms, descendants of semantic networks and KL-ONE, focusing on concepts, roles, and individuals. Learn about their formal semantics, decidable fragments of FOL, relationship to Propositional Modal & Dynamic Logics, provision of inference services, sound and complete decision procedures, and implemented systems.