Information Technology Reference
In-Depth Information
Definition 2.29
Formulas in DDL are defined as follows, where C is concept, R
is role, a, b are individual constants, and x, y are individual variables:
(1) C(
a
) and R(
a, b
) are called assertion formulas;
(2) C(
x
) and R(
x, y
) are called general formulas;
(3) Both assertion formulas and general formulas are all formulas;
(4) If
and
are formulas, then
¬
ϕ
,
ϕ
∧
,
ϕ
→
, and
∀
x
ϕ
are all
ϕ
formulas;
ϕ
is formula, then[
]
ϕ
is also formula.
(5) If
Definition 2.30
A finite set of {a
1
/x
1
, …, a
n
/x
n
} is an instance substitution, where
a
1
, …, a
n
are instance constants which are called substitution items, x
1
, …, x
n
are
variables which are called substitution bases, x
i
x
j
for each pair i, j i
n
{1, …, n}
such that i
j.
Definition 2.31
Let
ϕ
be a formula, let x
1
, …, x
n
be all the variables occurring
in
ϕ
, and let a
1
, …, a
n
be instance constants. If
ϕ
′
is a substitution result of
ϕ
with{a
1
/x
1
, …, a
n
/x
n
}, then
ϕ
′
is called a instance formula of
ϕ
.
Definition 2.32
A condition in DDL is an expression of the form:
∀
C, C(p), R(p,
q), p=q or p
q, where N
C
is a set of individual constants, N
X
is a set of
individual variables, N
I
is the union N
C
and N
X
, p,q
∈
N
I
, C is concept of DDL,
and R is role of DDL.
¬
A
(
x
,...,
x
)
≡
(
P
,
E
)
Definition 2.33
An action description is of the form
,
1
n
A
A
where,
