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from the known facts; all the facts that can be deduced are determined by facts
contained in the knowledge base. In the default logic, knowledge base can be
expanded with default knowledge so that more facts can be deduced; in spite that
these default knowledges maybe are unreliable.
Default rules used in default logic is of the following form:
α
(
x
) :
M
β
(
x
) , . . .,
M
β
(
x
)
1
m
(2.1)
W
(
x
)
It can also be represented as follows:
α
(
x
) :
M
β
(
x
), ...,
M
β
(
x
)
W
(
x
)
(2.2)
1
m
x
α
( )
x
Here
is a parameter vector,
is called the prerequisite of the default
i β is the default condition, and M is the
default operator. The default rule is to be read as “If the prerequisite
( )
rule,
is the consequent,
W x
( )
holds
α
( )
x
and it is concictent to assume
β β , then infer that the consequent
holds.” For example, consider the following default rule:
1 ( ),...,
x
( )
x
m
bird x M flies x
flies x
( ) :
( )
( )
It states that if x is a bird and it is consistent to assume that x can fly, then infer
that x can fly.
A default rule is closed if and only if none of
α
,
β
, ...,
β
,
W
contains a
1
m
free variable.
Definition 2.7
A default theory is a pair (D,W), where D is a set of default rules
and W a set of closed formulas.
A default theory (D,W) is closed iff every default rule contained in D is
closed. Default theory is nonmonotonic. For example, suppose T=<W, D> is a
:
MA
default theory with D={
} and W=∅, then the formula B can be derived
B
from T. However, if we add the knowledge ¬A into W and get the default theory
T'=<D, W'>, where W'={¬A}, then the formula B can not be derived from T'
any more, despite that T' is an extension of T together with W'⊇W.
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