Robotics Reference
In-Depth Information
statements to construct a logical argument, proving whatever one wishes
to prove or inferring whatever one wishes to infer. So if statements in
English or some other spoken language can be translated into the lan-
guage of logic, then the rules of logic can operate on those translations in
order to reason.
Reasoning is arguably one of the most important, if not
the
most
important, fundamental intellectual skill possessed by man. It allows us
to deduce and infer certain conclusions from evidence we already have.
It is the basis of being able to say that, because I am in London and there
are trains that go from London to Edinburgh, if I get on one of those
trains I can reach Edinburgh. It is the basis of being able to generalise,
to say that because the sun rose today and yesterday and for every day
in the past 100 years or more, that it will also rise tomorrow. These are
simple exercises in reasoning for humans, but how about for computers?
The creation of an artificial intellect on a par with or superior to our own
requires, amongst other things, a method by which that artificial intellect
can reason. The ability of computer programs to reason is absolutely vital
to the foundations of Artificial Intelligence.
The nineteenth-century English mathematician George Boole devel-
oped a mathematical analysis of the laws of human logic. He also de-
veloped an algebraic language (or notation) in which it is possible to
describe the interaction and relationship of
variables
that have only two
states—“true” and “false”. Boolean algebra, as it is now known, is based
on the three logical
operators
and
,
or
and
not
. The combination of
Boolean algebra and the rules of logic enables us to prove things “au-
tomatically”. That is to say, there is a process or method by which we
can use Boolean algebra, on statements that are derived from the rules of
logic, to create proofs—in other words, to reason.
Boolean Algebra provides part of such a method. It works on state-
ments such as
Aistrue
and
Bistrue
Aistrue
or
Bisfalse
Socrates is
not
awoman
“A”, “B”, “Socrates” and “woman” are the variables in these logical
statements.
When we try to prove something using the rules of logic we start with
two or more statements (called
premises
) and with a desired conclusion.