Information Technology Reference
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Before going on to this procedure, it is worthwhile to examine the notion of logical
entailment more closely. Recall that a sentence is
logically entailed
if it cannot not help
but be true if all the sentences in the knowledge base are true. In determining what
is and is not logically entailed, we do not use normal English understanding of the
constants that appear in the knowledge base or in the query. In the KB of figure 2.1,
there are constants like
sam
and
female
; for purposes of logical entailment, imagine
that these names have been changed everywhere to something neutral, like
object13
and
property51
.
Here are some sample logical entailments of this knowledge base:
jane is a child of sue.
This sentence is in the KB, and therefore if everything in the KB is true, it must
be true, too. Note that even if other symbols had been used everywhere in the
KB and in the query, like
relation17
instead of
child
and
person53
instead of
jane
,
the resulting sentence would still be an entailment.
sue is a parent of jane.
This sentence is not in the KB, but the following two sentences are there:
jane is a child of sue.
If X is a child of Y then Y is a parent of X.
So if everything in the KB is true, then by virtue of the special keywords
If
and
then
, the query must also be true. Again, this is not because of the relationship
between the English words
child
and
parent
; it is because there is a conditional
sentence in the KB that makes a connection between the
child
and
parent
symbols.
george is a grandfather of jane.
This sentence must be true for the same reason as the previous one; the argument
is just longer. It requires using these sentences in the KB:
1.
george is male.
2.
jane is a child of sue.
3.
sue is a child of george.
4.
If X is a child of Y then Y is a parent of X.
5.
If X is a child of Y and Y is male then Y is a father of X.
6.
If X is a father of Y and Y is a parent of Z then X is a grandfather of Z.
If everything in the KB is true, then the following sentences that are not in the
KB must also be true:
