Logic Foundation of Artificial Intelligence - Advanced Artificial Intelligence - page 95

2.12 Dynamic Description Logic

2.12.1 Description Logic

Description logic is a kind of formalization of knowledge representation based on
object, and it is also called concept representation language or terminological
logic. Description logic is a decidable subclass of first-order logic. It has
well-defined semantics and possesses strong expression capability. One
description logic system consists of four parts: constructors which represent
concept and role, TBox subsumption assertion, ABox instance assertion, and
reasoning mechanism of TBox and ABox. The representation capability and
reasoning capability of description logic system lie on aforementioned four
elements and different hypothesis (Baader, 2003).
There are two essential elements, i.e. concept and role, in description logic.
Concept is interpreted as subclass of domain. Role represents interrelation
between individuals, and it is a kind of binary relation of domain set.
In certain domain, a knowledge base K = <T, A> consists of two parts: TBox
T and ABox A. TBox is a finite set of subsumption assertions, and it is also
called terminological axiom set. The general format of subsumption assertion is
C ⊆ , where C and D are concepts. ABox is a finite set of instance assertions.
Its format is C(a), where a is individual name; or its format is P(a,b), where P is a
primitive role, a and b are two individual names.
In general, TBox is an axiom set which describes domain structure, and it
has two functions: one is to introduce concept name, the other is to declare
subsumption relationship of concepts. The process of introducing concept name
is expressed by A ԥ Cor

A ⊆ , where A is the concept which is introduced.
The format of subsumption assertion of concepts is

C

C ⊆ . As to concept
definition and subsumption relation definition, the following conclusion comes
into existence:

D

C ԥ D Ӈ C գ D and C գ D .

ABox is an instance assertions set, and its function is to declare attribute of
individual or relationship of individuals. There are two kinds of format: one is to
declare the relationship of individual and concept, the other is to declare the
relationship of two individuals. In ABox, as to arbitrary individual a and concept
C, the assertion which decides whether individual a is member of concept C is