<s>
In	O
mathematical	O
logic	O
,	O
a	O
predicate	B-Algorithm
variable	I-Algorithm
is	O
a	O
predicate	O
letter	O
which	O
functions	O
as	O
a	O
"	O
placeholder	O
"	O
for	O
a	O
relation	O
(	O
between	O
terms	O
)	O
,	O
but	O
which	O
has	O
not	O
been	O
specifically	O
assigned	O
any	O
particular	O
relation	O
(	O
or	O
meaning	O
)	O
.	O
</s>
<s>
Common	O
symbols	O
for	O
denoting	O
predicate	B-Algorithm
variables	I-Algorithm
include	O
capital	O
roman	O
letters	O
such	O
as	O
,	O
and	O
,	O
or	O
lower	O
case	O
roman	O
letters	O
,	O
e.g.	O
,	O
.	O
</s>
<s>
In	O
higher-order	B-Algorithm
logic	I-Algorithm
,	O
predicate	B-Algorithm
variables	I-Algorithm
correspond	O
to	O
propositional	O
variables	O
which	O
can	O
stand	O
for	O
well-formed	O
formulas	O
of	O
the	O
same	O
logic	O
,	O
and	O
such	O
variables	O
can	O
be	O
quantified	O
by	O
means	O
of	O
(	O
at	O
least	O
)	O
second-order	O
quantifiers	B-Language
.	O
</s>
<s>
Predicate	B-Algorithm
variables	I-Algorithm
should	O
be	O
distinguished	O
from	O
predicate	O
constants	O
,	O
which	O
could	O
be	O
represented	O
either	O
with	O
a	O
different	O
(	O
exclusive	O
)	O
set	O
of	O
predicate	O
letters	O
,	O
or	O
by	O
their	O
own	O
symbols	O
which	O
really	O
do	O
have	O
their	O
own	O
specific	O
meaning	O
in	O
their	O
domain	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
:	O
e.g.	O
</s>
<s>
If	O
letters	O
are	O
used	O
for	O
both	O
predicate	O
constants	O
and	O
predicate	B-Algorithm
variables	I-Algorithm
,	O
then	O
there	O
must	O
be	O
a	O
way	O
of	O
distinguishing	O
between	O
them	O
.	O
</s>
<s>
One	O
possibility	O
is	O
to	O
use	O
letters	O
W	O
,	O
X	O
,	O
Y	O
,	O
Z	O
to	O
represent	O
predicate	B-Algorithm
variables	I-Algorithm
and	O
letters	O
A	O
,	O
B	O
,	O
C	O
,...,	O
U	O
,	O
V	O
to	O
represent	O
predicate	O
constants	O
.	O
</s>
<s>
This	O
is	O
the	O
first	O
step	O
towards	O
creating	O
a	O
higher-order	B-Algorithm
logic	I-Algorithm
.	O
</s>
<s>
If	O
the	O
predicate	B-Algorithm
variables	I-Algorithm
are	O
not	O
defined	O
as	O
belonging	O
to	O
the	O
vocabulary	O
of	O
the	O
predicate	O
calculus	O
,	O
then	O
they	O
are	O
predicate	O
metavariables	O
,	O
whereas	O
the	O
rest	O
of	O
the	O
predicates	O
are	O
just	O
called	O
"	O
predicate	O
letters	O
"	O
.	O
</s>
<s>
If	O
"	O
predicate	B-Algorithm
variables	I-Algorithm
"	O
are	O
only	O
allowed	O
to	O
be	O
bound	O
to	O
predicate	O
letters	O
of	O
zero	O
arity	O
(	O
which	O
have	O
no	O
arguments	O
)	O
,	O
where	O
such	O
letters	O
represent	O
propositions	O
,	O
then	O
such	O
variables	O
are	O
propositional	O
variables	O
,	O
and	O
any	O
predicate	O
logic	O
which	O
allows	O
second-order	O
quantifiers	B-Language
to	O
be	O
used	O
to	O
bind	O
such	O
propositional	O
variables	O
is	O
a	O
second-order	O
predicate	O
calculus	O
,	O
or	O
second-order	O
logic	O
.	O
</s>
<s>
If	O
predicate	B-Algorithm
variables	I-Algorithm
are	O
also	O
allowed	O
to	O
be	O
bound	O
to	O
predicate	O
letters	O
which	O
are	O
unary	O
or	O
have	O
higher	O
arity	O
,	O
and	O
when	O
such	O
letters	O
represent	O
propositional	B-Algorithm
functions	I-Algorithm
,	O
such	O
that	O
the	O
domain	O
of	O
the	O
arguments	O
is	O
mapped	O
to	O
a	O
range	O
of	O
different	O
propositions	O
,	O
and	O
when	O
such	O
variables	O
can	O
be	O
bound	O
by	O
quantifiers	B-Language
to	O
such	O
sets	O
of	O
propositions	O
,	O
then	O
the	O
result	O
is	O
a	O
higher-order	B-Algorithm
predicate	I-Algorithm
calculus	O
,	O
or	O
higher-order	B-Algorithm
logic	I-Algorithm
.	O
</s>
