Information Technology Reference
In-Depth Information
Definition 2.38
(primitive action or complex action), if there
exists an interpretation I(u) = (
Given action
ŋ
,
•
I(u)
Ș
) corresponding to ABox A, and an
,
•
I(v)
Ș
→
interpretation I(v) = (
) corresponding to ABox A and TBox T, and u
v
is satisfied, then action a is realizable corresponding to ABox A.
Definition 2.39
(primitive action or complex
action), as to arbitrary interpretations I(u) = (
Given two actions
ŋ
and
Ȳ
,
•
I(u)
,
•
I(v
Ș
) and I(v) = (
Ș
)), the
→
→
following condition is satisfied: if the existence of u
v can make u
v
β
come true, then action
Ȳ
subsumes action
ŋ
, denoted as
ŋ
Ȳ
.
⊆
Definition 2.40
ŋ
Ȳ
Given two actions
and
(primitive action or complex
,
•
I(u)
Ș
) corresponding to ABox A of
action), an arbitrary interpretation I(u) = (
,
•
I(v)
DDL, and an arbitrary interpretation I(v) = (
) corresponding to ABox A
and TBox T, the following condition is satisfied: if the existence of u
Ș
→
v can
→
makeu
v come true, then action
Ȳ
subsumes action
ŋ
corresponding to
β
ABox A, denoted as
ŋ
⊆
A
Ȳ
.
Remark.
Similar to Definition 2.38 and Definition 2.40, action realization or
subsumption corresponding to TBox T may also be defined. In order to
understand the action subsumption, the following is a simple example.
Given four action descriptions:
1
= ({A(
a
), ¬A(
b
)}, {
⁄¬A(
a
),
⁄A(
b
)})
、
2
= ({A(
c
), ¬A(
d
)}, {
⁄¬A(
c
),
⁄A(
d
)}),
3
= ({A(
x
), ¬A(
y
)}, {
⁄¬A(
x
),
⁄A(
y
)})
and
4
= ({A(
y
), ¬A(
x
)}, {
⁄¬A(
y
),
⁄A(
x
)}), where
a ,b, c, d
are individual
constants, and
x, y
are individual variables, then we have
,
,
a
⊆
a
a
⊆
a
1
3
2
3
,
,
and
, but there is no subsumption relation
a
⊆
a
a
⊆
a
a
⊆
a
a
⊆
a
1
4
2
4
3
4
4
3
between
1
and
2
.
Exercises
1.
What is monotonic reasoning? What is nonmonotonic reasoning?
2.
How is default rules represented in default theory? What representation forms
does there exist?
3.
A default theory is a pair T=<W, D>, with D a set of default rules and W a set
of closed formulas. Please represent the following sentences with such a
default theory.
