Boolean logic can be thought of as a very simple number system, given our original framework; a boolean description is a quantitative description. Conjunction and disjunction are often thought of as multiplication and addition, respectively. Both are associative and commutative. Both distributive laws are obeyed:
is an identity for conjunction while
is an identity for disjunction.
Neither operator is invertible. The numbers
can be ordered by agreeing that 
.
Three valued logic is isomorphic to 
.
The mapping 
,
and
.
We let 
denote that
b is a valid description of a, where a and b are members
of 
:
are members of .
All of the properties of three valued logic can be
deduced from this, together with the properties
of boolean logic. This is the spirit behind
three valued logic: 
symbolizes a lack of knowledge.
With further knowledge each can be reduced
to either or .
| Jeff Tupper | March 1996 |