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George is male and Sue is a child of George, so George is a father of Sue.
Furthermore, John is a child of Sue, so Sue is a parent of John.
Putting these two facts together, George is a father of Sue, who is a parent of
John. So George is a grandfather of John.
2.5 Why is back-chaining good?
Why is back-chaining a procedure worth studying? There are really two issues here:
Why do we want to do logical entailment at all? This is not an unreasonable
question. A lot of what is called thinking seems to be quite unlike what is called
logic. All one can say about this for now is that at least some simple forms of
thinking (like figuring out grandfathers) do appear to involve extracting logical
entailments from other things that are known.
Is back-chaining the only way to compute logical entailments?. The answer is
no. There is also
forward-chaining
as well as other procedures that have little to
do with chaining. Moreover, back-chaining is only defined for knowledge bases
consisting of atomic and conditional sentences. If one wants to deal with negation
or disjunction or any other connectives in the knowledge base, one would need
to use another procedure (see chapter 11).
What then is so good about back-chaining?
It is
goal-directed
. One works backward from a goal (the query to be established)
toward what is known (the atomic sentences). In forward-chaining, one starts
with atomic sentences and then using the conditional sentences to get new atomic
sentences, continues looking for new conclusions, hoping to eventually hit the
query. So forward-chaining is looser, more like free association. In some cases,
this is good, but with a specific target in mind (the query), it can be unfocused
and wasteful.
It is
logically sound
. To say that a procedure is logically sound means that any
time it returns
success
to a query, the query is indeed logically entailed by the
knowledge base. In other words, it never makes a mistake. Back-chaining has
this property (so far).
It is sometimes
logically complete
. To say that a procedure is logically complete
means that any time a query is logically entailed by the knowledge base, the
procedure will eventually return
success
. In other words, the procedure does
