Information Technology Reference
In-Depth Information
Figure 2.1.
A family example knowledge base
john is a child of sue.
john is a child of sam.
jane is a child of sue.
jane is a child of sam.
sue is a child of george.
sue is a child of gina.
john is male.
jane is female.
june is female.
sam is male.
sue is female.
george is male.
If X is a child of Y then Y is a parent of X.
If X is a child of Y and Y is male then Y is a father of X.
If X is male and Y is female then X is of opposite sex from Y.
If X is male and Y is female then Y is of opposite sex from X.
If X is a father of Y and Y is a parent of Z then X is a grandfather of Z.
In both cases, the sentences may contain variables (written here capitalized) and
constants (written here uncapitalized). So, for example,
sue is a child of george.
is an example of an atomic sentence, whereas
If X is a child of Y and Y is male then Y is a father of X.
is an example of a conditional sentence. In these two sentences, the words
If
,
and
,
and
then
are special keywords,
X
and
Y
are variables, and all the other words are
considered to be constants.
A complete but small KB in this restricted sublanguage of English is shown in
figure 2.1. In this case, the first five lines are atomic sentences (a total of twelve of
them), and the remaining five lines are conditional sentences.
At this point, you should not spend too much time trying to make sense of the
sentences. They will be treated as a collection of symbols, somewhat like the digits in
an arithmetic problem.
2.2 Logical entailment
The computational procedure of interest here is one that computes logical entailments
of a knowledge base. More precisely, the procedure will receive an atomic sentence
Q
(the
query
) as input, and its job will be to determine if the query is logically entailed
by the knowledge base.
