Family of Logic Based KR Formalisms

12 Questions

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

Concepts (classes), roles (relationships), individuals

What distinguishes the family of logic-based KR formalisms?

Formal semantics, decidability, provision of inference services

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

Ron Brachman (AT&T Labs)

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

KL-ONE, NIKL, KANDOR

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

DAML+OIL, OWL

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

Ontologies, terminological knowledge, database schemata

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

Primitive concepts have only necessary properties, while defined concepts have necessary and sufficient conditions.

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

Individuals are treated the same as constants in First-Order Logic (FOL), concepts are treated the same as Unary Predicates in FOL, and roles are treated the same as Binary Predicates in FOL.

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

The basic unit is the Description, which describes sets of individuals.

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?

HappyFather = Man ∩ ∃hasChild.Female ∩ ∃hasChild.Male ∩ ∀hasChild.(Rich ∪ Happy)

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

TBox refers to the Terminology Box which defines concepts, and ABox refers to the Assertion Box which contains assertions about individuals.

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

Higher expressiveness implies higher complexity.

Study Notes

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.