Information Technology Reference
In-Depth Information
Before action of DDL is defined, state transition (one state transits to other state
under action) is defined first.
Definition 2.36
,
•
I(u)
,
•
I(v)
Given two interpretations I(u) = (
Ș
) and I(v) = (
Ș
),
under state u and v, an action
ŋ
= (P
ŋ
,E
ŋ
) can produce state v when applied
α
X
→
N
Ș
to state u (written u
v ), if there exists an assignment map
γ
.
→
, such
that
γ
, I(u) and I(v) satisfy the following conditions:
(1) I(u) and γ satisfy each condition of pre-conditions P
;
(2) as to each pair head/body of post-conditions E
, if I(u) and γ satisfy head,
then I(v) and γ satisfy body.
In this case, we can say that action
can produce state v when applied to state
u and assignment map γ, and it is denoted as u
γ
→
v.
The semantics of atomic and complex actions are defined as follows:
γ
α
→
·
= {<
u
,
v
> |
u
,
v
∈
W
,
u
v
};
γ
α
→
→
γ
β
·
;
= {<
u
,
v
> |
u
,
v
,
w
∈
W
,
u
w
∧
w
v
};
γ
α
→
→
γ
β
·
֖
= {<
u
,
v
> |
u
,
v
∈
W
,
u
v
∨
u
v
};
γ
α
→
→
γ
→
γ
·
*= {<
u
,
v
> |
u
,
v
∈
W
,
u
v
∨
u
v
∨
u
v
∨ …};
α;
α
α
;
α
;
α
u
պϕ
}.
Because aforementioned action interpretation is based on description logic,
some new concepts about action may be given, and these new concepts
supplement description logics.
·
ϕ
? = {<
u
,
u
> |
u
∈
W
,
Definition 2.37
Given action
ŋ
(primitive action or complex action), if there exist
,
•
I(u)
,
•
I(v)
→
two interpretations I(u) = (
Ș
) and I(v) = (
Ș
) that satisfy u
v, then
action
ŋ
is realizable.
