<s>
In	O
the	O
formal	O
sciences	O
,	O
the	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
,	O
also	O
called	O
the	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
,	O
universal	O
set	O
,	O
or	O
simply	O
universe	O
,	O
is	O
the	O
set	O
of	O
entities	O
over	O
which	O
certain	O
variables	O
of	O
interest	O
in	O
some	O
formal	O
treatment	O
may	O
range	O
.	O
</s>
<s>
The	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
is	O
usually	O
identified	O
in	O
the	O
preliminaries	O
,	O
so	O
that	O
there	O
is	O
no	O
need	O
in	O
the	O
further	O
treatment	O
to	O
specify	O
each	O
time	O
the	O
range	O
of	O
the	O
relevant	O
variables	O
.	O
</s>
<s>
Many	O
logicians	O
distinguish	O
,	O
sometimes	O
only	O
tacitly	O
,	O
between	O
the	O
domain	O
of	O
a	O
science	O
and	O
the	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
of	O
a	O
formalization	O
of	O
the	O
science	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
an	O
interpretation	O
of	O
first-order	O
logic	O
,	O
the	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
is	O
the	O
set	O
of	O
individuals	O
over	O
which	O
the	O
quantifiers	B-Language
range	O
.	O
</s>
<s>
A	O
proposition	O
such	O
as	O
is	O
ambiguous	O
,	O
if	O
no	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
has	O
been	O
identified	O
.	O
</s>
<s>
In	O
one	O
interpretation	O
,	O
the	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
could	O
be	O
the	O
set	O
of	O
real	O
numbers	O
;	O
in	O
another	O
interpretation	O
,	O
it	O
could	O
be	O
the	O
set	O
of	O
natural	O
numbers	O
.	O
</s>
<s>
If	O
the	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
is	O
the	O
set	O
of	O
real	O
numbers	O
,	O
the	O
proposition	O
is	O
false	O
,	O
with	O
as	O
counterexample	O
;	O
if	O
the	O
domain	O
is	O
the	O
set	O
of	O
natural	O
numbers	O
,	O
the	O
proposition	O
is	O
true	O
,	O
since	O
2	O
is	O
not	O
the	O
square	O
of	O
any	O
natural	O
number	O
.	O
</s>
<s>
The	O
term	O
"	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
"	O
generally	O
refers	O
to	O
the	O
collection	O
of	O
objects	O
being	O
discussed	O
in	O
a	O
specific	O
discourse	O
.	O
</s>
<s>
In	O
model-theoretical	O
semantics	O
,	O
a	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
is	O
the	O
set	O
of	O
entities	O
that	O
a	O
model	O
is	O
based	O
on	O
.	O
</s>
<s>
The	O
concept	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
is	O
generally	O
attributed	O
to	O
Augustus	O
De	O
Morgan	O
(	O
1846	O
)	O
but	O
the	O
name	O
was	O
used	O
for	O
the	O
first	O
time	O
by	O
George	O
Boole	O
(	O
1854	O
)	O
on	O
page	O
42	O
of	O
his	O
Laws	O
of	O
Thought	O
.	O
</s>
