Robotics Reference
In-Depth Information
What is Logic?
In Chapter 1 we saw how the science of logic was first mechanized in
a number of devices, built mostly in the nineteenth century, to solve
simple problems. To recap a little, the underlying foundation of logic is
the question of whether a particular statement is true or false, and those
nineteenth-century devices represented truth and falsity in a visual way
that was easy for the user to follow. For example, in Jevons' abacus
1
the
presence in a vertical rack of a wooden tile indicated that a statement
corresponding to that tile was true.
The mechanical methods for solving simple logic problems were given
a boost, in 1854, when the British mathematician George Boole devised
Boolean algebra, a system of logic based on the three fundamental op-
erators:
not
,
and
and
or
.
2
Boole was able to express his system of logic
in mathematical formulae that could be manipulated and subsequently
simplified, but he could hardly have imagined the great power his system
would one day wield, becoming the basis of logic as it is used for compu-
tation. Because logic allows us to describe situations and knowledge in a
way that can be understood and manipulated by computers, it allows us
also to represent problems that we want to solve and to use its rules to
enable us to find the solutions to these problems.
The language of logic, unlike spoken language, is precise and unam-
biguous. For example, the statement
Everyone in my family likes a cat
is ambiguous. Does it mean that everyone in my family likes a particular
cat, or that everyone likes a different cat (one cat per person), and which
cat for which person? In logic we would need to express our intended
meaning of this statement in a more precise way, for example,
Everyone in my family likes at least one particular cat called Muffin.
This level of precision is necessary in computer programs if they are to
avoid going down blind alleys in their search for the solutions to prob-
lems. And once we have this level of precision in our premises (the state-
ments on which a logical argument depends), we can express the situation
or problem in a precise and compact way for programming. For example,
1
See the section “Nineteenth-Century Logic Machines” in Chapter 1.
2
See the section “Early Logic Machines” in Chapter 1.
