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name. Thus, for a knowledge base
K
=(
U
,
R
) and a knowledge representation
system
S
=(
U
,
A
), the relation between them is: if
r
∈
R
and
U
|
r
={
x
1
,
x
2
, ···,
x
n
},
then for attribute set
A
and each attribute
a
r
:
U
¼
V
a
, we have
V
a
= {1,2, ···,
k
}, and
a
r
(
). Therefore, all the notions about knowledge base can
be described by the definition of knowledge representation systems.
Thus, any equivalence relation within the knowledge base can be represented
by an equivalence class of relations expressed by attributes and attribute values in
the data table of the knowledge system. The columns in the table can be viewed
as names of some categories, and the whole table includes the description of all
categories within the corresponding knowledge base and all possible rules that
can be deducted from the data in the table. Thus, data table of knowledge
representation system is the description of valid facts and rules in the knowledge
base.
A decision table can be seen as a special and important knowledge
representation system. It shows that, when some conditions are satisfied, how
decisions, actions, operations, or controls can be made. Most of decision
problems can be expressed by decision tables, thus the tools plays an important
role in the application of decision.
Decision tables can be defined as follows according to the definition of
knowledge representation systems.
S
x
)=
i
iff
x
∈
X
i
, (
i
=1,2, ···,
k
are two
attribute subsets, which are called condition attribute subset and decision
attribute subset respectively. The knowledge representation systems having
condition attributes and decision attributes can be expressed by decision tables,
denoted as
=(
U
,
A
) is a knowledge representation system, and
C
、
D
⊂
A
T
=(
U
,
A
,
C
,
D
) and called as
CD
decision tables for short. The
equivalence classes of relation
IND
(
C
) and
IND
(
D
) are called condition classes
and decision classes respectively.
11.3.2
Decision Logic Language
In this chapter, we view data tables as special logic models, called as decision
logic. They infer conclusions according to the knowledge acquiring from
knowledge representation systems. And, we will use symbol tools of logic
deduction to discover knowledge dependency and to reduce knowledge.
Although algorithms are usually a series of statements, we still use the term
“decision algorithms” to represent a set of decision rules, because decision logic
is our main focus. Moreover, as a set of formulas, the decision algorithms do not
