Information Technology Reference
In-Depth Information
v
Here,
v
i
•
,{
a
1
,a
2
, ··· ,a
n
}⊆
P
and
P
⊆
A
. Above formalized formula is called
a
as
P
basic formula. For attribute set
A
, above formalized formula is called as
A-basic formula.
Given that
P
⊆
A
, a
P
-formula θ and
x
∈
U,
if
x|=
θ, θ is called as the
P-
expression of
. This is similar with the introduction in previous section,
which uses condition attribute sets to describe objects.
In a knowledge representation system
x
in
S
S
=(
U,A
), all sets satisfying
A
-basic
formula are called as basic knowledge in
S.
Ã
(
P
) denotes the decompositions in
S
that satisfying
P
-formula. If
P
=
A
and
the eigenformula of
S
=(
U
,
A
) is defined as
Ã
(
A
), then
Ã
(
A
) represents the
decompositions in
S
that satisfying
A
-formula, and it is a token of all the
knowledge in
S.
Specifically, each row in our language table can be expressed by
a given
A
-basic formula, and the whole table is described by all this kind of
formulas.
In the following, we give some axioms of decision logics:
(1) For each
a
∈A,
v, u
∈V
a
, and
v
≠
u
(
a,v
)∧(
a,u
)≡0;
(2) For each
a
∈A and
v
∈V
a
∨(
a,v
)≡1;
(3) For each
a
∈A,
u
∈V
a
and
v
≠
u
, ∼(
a,v
)≡∨(
a,u
).
is based on the assumption: for each attribute, each object only
has an exact value on it. For example, if a material is red, it cannot be blue or
green.
Axiom (1)
Axiom (2)
is based on the assumption: for each attribute, each object in
system must have a value field on it. For example, if an attribute is a description
of color, then an object with the attribute must have a color. The color is the
value of this attribute.
Axiom (3)
is to show that negative words can be omitted. If an object has
some property, then we cannot say it does not have other properties. For
example, we can say a material is green or blue, but we cannot say it is not red.
Proposition 11.3
For each P
⊆
A, |=S
Ã
S(P)
≡
1.
Proposition 11.3 shows that the knowledge in knowledge representation
system is all that can be acquired currently. It corresponds to the so called closed
word assumption.
If and only if formula θ can be inferred from the axioms and formulas of
formula Ω, we call θ as a formula inferred from Ω, denoted as Ω |
θ. If θ can be
