<s>
In	O
predicate	O
logic	O
,	O
universal	B-Algorithm
instantiation	I-Algorithm
(	O
UI	O
;	O
also	O
called	O
universal	B-Algorithm
specification	I-Algorithm
or	O
universal	B-Algorithm
elimination	I-Algorithm
,	O
and	O
sometimes	O
confused	O
with	O
dictum	O
de	O
omni	O
)	O
is	O
a	O
valid	O
rule	O
of	O
inference	O
from	O
a	O
truth	O
about	O
each	O
member	O
of	O
a	O
class	O
of	O
individuals	O
to	O
the	O
truth	O
about	O
a	O
particular	O
individual	O
of	O
that	O
class	O
.	O
</s>
<s>
It	O
is	O
generally	O
given	O
as	O
a	O
quantification	B-Language
rule	O
for	O
the	O
universal	O
quantifier	B-Language
but	O
it	O
can	O
also	O
be	O
encoded	O
in	O
an	O
axiom	O
schema	O
.	O
</s>
<s>
It	O
is	O
one	O
of	O
the	O
basic	O
principles	O
used	O
in	O
quantification	B-Language
theory	O
.	O
</s>
<s>
Irving	O
Copi	O
noted	O
that	O
universal	B-Algorithm
instantiation	I-Algorithm
"	O
follows	O
...	O
from	O
variants	O
of	O
rules	O
for	O
'	O
natural	O
deduction	O
 '	O
,	O
which	O
were	O
devised	O
independently	O
by	O
Gerhard	O
Gentzen	O
and	O
Stanisław	O
Jaśkowski	O
in	O
1934.	O
"	O
</s>
<s>
According	O
to	O
Willard	O
Van	O
Orman	O
Quine	O
,	O
universal	B-Algorithm
instantiation	I-Algorithm
and	O
existential	O
generalization	O
are	O
two	O
aspects	O
of	O
a	O
single	O
principle	O
,	O
for	O
instead	O
of	O
saying	O
that	O
"	O
∀xx	O
=	O
x	O
"	O
implies	O
"	O
Socrates	O
=	O
Socrates	O
"	O
,	O
we	O
could	O
as	O
well	O
say	O
that	O
the	O
denial	O
"	O
Socrates≠Socrates	O
"	O
implies	O
"	O
∃xx≠x	O
"	O
.	O
</s>
<s>
The	O
principle	O
embodied	O
in	O
these	O
two	O
operations	O
is	O
the	O
link	O
between	O
quantifications	B-Language
and	O
the	O
singular	O
statements	O
that	O
are	O
related	O
to	O
them	O
as	O
instances	O
.	O
</s>
