Information Technology Reference
In-Depth Information
Table 2.3 Syntax and semantics of ALC
Constructor
Syntax
Semantics
Example
A
I
I
Primitive concept
A
Human
P
I
¥
I
×
I
P
rimitive concept
P
has-child
I
top
⊥
True
Bottom
⊥
False
C
I
D
I
intersection
C
D
Human
Male
C
I
D
I
Union
C
D
Doctor
Lawyer
I
-C
I
Negation
¬C
¬Male
Existential
quantification
{x|
"
y
, (
x, y
)
∈
R
I
∧
y
∈
C
I
}
"
has-child.Male
"
R.C
{x|
y
,(
x, y
)
∈
R
I
×
y
∈
C
I
}
has-child.Male
Value restriction
R.C
The basic reasoning problems of description logic include concept
satisfiability, concept subsumption relation, instance checking, consistency
checking and so on, where the concept satisfiability is the most basic reasoning
problem, other reasoning problem may be reduced to concept satisfiability
problem.
In description logic, reasoning problem may be reduced to concept
satisfiability problem through the following properties. As to concept C, D, there
exists the following proposition:
(1) C
¥
D
⇔
C
∩
¬D is unsatisfiable;
(2) C
ԥ
D (concept C and D are equivalent)
⇔
both (C
∩
¬D) and (D
∩
¬C)
are unsatisfiable;
(3) C and D are disjoint
±
C
∩
D is unsatisfiable.
