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The following proposition proposes some simple properties related with
above concepts.
Proposition 11.2
If and only if | θ | S =U,|= S θ ;
(1)
If and only if | θ | S = ,|= S ~ θ ;
(3)
(2)
If and only if | θ | S | ϕ | S ,|= S θ → ϕ ;
If and only if | θ | S =| ϕ | S ,|=S ϕ .
(4)
At last, we should emphasize that the meaning of formulas depends on the
understanding of the knowledge in universe, that is, depends on the knowledge
representation systems. Especially, although a formula can be true in a
knowledge representation system, it can be false in another knowledge
representation system. In our research, they make special sense.
11.3.4 Deduction of Decision Logic
In above sections, we use language to describe the knowledge included in a
special knowledge representation system. Although for many knowledge
representation systems, different object sets can be used to the common language
processing, but we still use the coordinate sets of attributes and their values to
process. From the viewpoints of Semeiology, all the languages of these systems
are coordinate. However, according to the sets of different objects, their
semantics are diverse and the properties expressed by their appointed knowledge
representation systems are also different.
All axiom sets of decision logic are constructed by proposition repetition
logic and some special theorems. Before presenting the axioms of knowledge
representation systems, we first introducing some assistant concepts, which are
written as follows for short:
θ
= df 0
θ
= df 1
Apparently, |=1 and |=
0. Thus, 1 and 0 represent true or false respectively.
Usually, a formalized formula is defined as follows:
(
~
,v
1 ) ( a 2 ,v 2 ) ··· ( a n ,v n )
a
1
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