Information Technology Reference
In-Depth Information
I
(
u
)
×
;
·
R
)
I
(
u
)
=
−
C
I
(
u
)
· (¬
C
;
)
I
(
u
)
=
×
−
R
I
(
u
)
· (¬
R
;
)
I
(
u
)
=
I
(
u
)
I
(
u
)
C
ե
D
֕
D
· (
C
;
)
I
(
u
)
=
I
(
u
)
I
(
u
)
C
զ
D
֖
D
· (
C
;
)
I
(
u
)
= {
I
(
u
)
I
(
u
)
· (∃
R
.
C
x
| ∃
y
.((
x
,
y
)∈
R
∧
y
∈
C
)};
)
I
(
u
)
= {
I
(
u
)
I
(
u
)
¼
· (∀
R
.
C
x
| ∀
y
.((
x
,
y
)∈
R
y
∈
C
)};
)
I
(
u
)
= {
)
I
(v)
}.
· ([
]
C
x
|
uT
α
v
∧
x
∈(
C
Since the interpretation of the objects name does not depend on the particular
world, we use the rigid designator and assume that each name of individual is
uniform and does not change with state changing. Usually we write aI(u) as a for
short.
Given action
A
X
A
(
x
,...,
x
)
≡
(
P
,
E
)
N
is all variable set which happened
in action A, I = (
I
,·I)is an interpretation, and map γ:
,
1
n
A
A
I
is an variable
evaluation which happened in action A. As to individual constant a∈N
C
of ABox
of DDL, ·
I
interprets a as an element of
I
, i.e. aI
∈
A
X
N
→
I
. As to individual variable
or individual constant p∈N
I
, their interpretation is given in the following:
γ
(
if
if
,
p
)
p
∈
N
Ê
=
Ë
X
p
I
,
γ
I
p
p
∈
N
Ì
C
then the condition interpretations of DDL are as follows:
· If
I
=
I
, then
C
I
and γ satisfy condition∀
C
;
I,
γ
∈
C
I
, then
· If
a
I
and γ satisfy condition C(a);
I,
γ
=
I,
γ
, then
· If
a
b
I
and γ satisfy condition
a = b
;
I,
γ
I,
γ
, then
· If
a
b
I
and γ satisfy condition
a # b
;
I,
γ
,
I,
γ
>∈
R
I
, then
).
In each state u, assertion formulas connect individual constants to concepts
and roles. So there are two kinds of assertion formulas, concept assertions with
the form of C(a) and role assertions with the form of R(a
1
, a
2
). As to concept
· If<
a
b
I
and γ satisfy condition
R
(
a
,
b
