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inferred from axioms uniquely, θ is called a theorem of decision logic, written as
|θ for short.
If and only if formula θ
∧
~θ
cannot be inferred from formula Ω, the set of Ω
is called as consistent.
11.3.5
Standard Expression
The formulas in knowledge representation language can be expressed by a kind
of standard expressions, which are similar with classical propositions.
Let
be an attribute subset and θ be a formula in knowledge
representation language. If and only if θ
=
∅
or θ=1, or θ is a decomposition of a
non-empty P-basic formula in
P
⊆
A
, we call θ as a P-standardized form in
S
. A-
standardized expressions are called standardized formulas.
Proposition 11.4
S
Given
θ
which is a formula in decision logic language, and P
which includes all attributes of
θ
, if axioms (1) to (3) and formula
S(A) are
satisfied, then there is only one formula
ψ
in P form of criterion satisfying |
θ≡ψ
.
It is obvious that, we can calculate a formula's form of criterions by inferring
propositions and transforming some axioms of knowledge representation systems.
Ã
11.3.6
Decision Rules and Algorithms
In logic language, θ→Ψ is called as a decision rule in knowledge representation
languages. Here, θ and Ψ are named as the premise and consequence of the
decision rule respectively, which is similar with the condition attributes and
decision attributes we used to describe objects. Decision rule is to express a kind
of cause-and-effect relations.
If θ→Ψ is true in
, otherwise inconsistent.
If a decision rule is consistent in S, identical premises must infer to identical
consequences; but identical consequences may not be inferred by identical
premises.
Given
S
, we say the rule is consistent in
S
P
and
Q
, if θ→Ψ is a decision rule, and θ, Ψ are P-basic formula and
Q
-basic formula respectively, then θ→Ψ is called as a
PQ
-basic decision rule or
PQ
-attributes can be viewed as the
condition attributes and decision attributes we explored before.
rule for short. Here,
P
-attributes and
Q
