Information Technology Reference
In-Depth Information
2
A Procedure for Thinking
Chapter 1 showed that thinking, or at least some simple forms of thinking, could
be profitably understood as drawing conclusions from a large collection of sentences
called a knowledge base (KB). Leibniz's idea was that the rules of logic would tell how
to manipulate these symbolic structures representing propositions the same way that
the rules of arithmetic tell how to manipulate symbolic structures representing num-
bers. This chapter examines this symbolic manipulation as a computational
procedure
,
not so different from those for arithmetic.
The procedure studied in this chapter is called
back-chaining
. It works on sentences
of English, but sentences that are very restricted in their form. They have none of
the niceties found in English or any other natural language. On the other hand, these
sentences can be treated as
uninterpreted
symbolic structures: one can operate on them
without having to know in advance what they mean. This is in accordance with the
view of computation saying that one can produce interesting answers to interesting
questions without having to know what the symbols stand for.
This chapter has five sections. The first section looks at the types of sentences
included in the knowledge base and introduces a small example. Section 2 examines
the notion of logical entailment in a bit more detail. The back-chaining procedure is
presented in section 3. Section 4 looks at some complex behavior of back-chaining
involving variables. Section 5 summarizes very briefly what is good and less good
about this procedure for thinking.
2.1 Atomic and conditional sentences
A special but very useful case of a knowledge base is one consisting of just two sorts
of sentences:
Atomic sentences,
that is,
simple basic sentences whose exact form is left
unspecified for now
Conditional sentences, that is, sentences of the form
If
P
1
and
...
and
P
n
then
Q
,
where the
P
i
and the
Q
are atomic sentences
