A Procedure for Thinking - Thinking as Computation - page 31

indentation was used to show how deep you were in the procedure. When one of the
subqueries returns success or failure , you must be able to decide what to do at one
level higher.
This is illustrated in example 3 with the subquery sue is a child of george . This
subquery returned success . But the work was not finished, since at a higher level, it
was still necessary to work on the second subquery george is male .
In example 4, the first conditional sentence found did not work: the subquery jane
is male returned failure . But again the work was not finished: the procedure was at
step 3, and it required going to step 4, which required returning to step 2 to look for
another conditional. The second conditional did work, and the entire query returned
success .
2.4 Variables in queries
In the four examples just considered, the query Q only contained constants. The
back-chaining procedure must be generalized so that it also works when Q contains
variables. In this case, the interest lies not in whether Q is logically entailed, but for
what values of the variables the query Q is logically entailed. Note the following:
If the query is sue is a child of gina , it asks if the sentence is logically entailed
by the KB. It is a yes/no question, and the success or failure returned by back-
chaining gives the answer.
If the query is X is a child of gina , it asks for what value of X is the sentence
logically entailed by the KB. It is a wh question (who? what? when? where?
why? how?). The expected answer is something like X=sue (since the sentence
sue is a child of gina is entailed).
When a query contains a variable, a unique answer is not necessarily expected. If the
query is john is a child of Z , either of the following answers would work: Z=sue or
Z=sam ; each corresponding sentence is logically entailed.
2.4.1 One complication: Renaming variables
One complication raised by the issue of variables within queries is the following: what
should be done if a variable in a query has the same name as one in the knowledge
base? How can one keep straight which is which?
The answer is simple: