<s>
In	O
logic	O
,	O
a	O
predicate	B-Algorithm
is	O
a	O
symbol	O
that	O
represents	O
a	O
property	O
or	O
a	O
relation	B-Algorithm
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
the	O
first-order	O
formula	O
,	O
the	O
symbol	O
is	O
a	O
predicate	B-Algorithm
that	O
applies	O
to	O
the	O
individual	O
constant	O
.	O
</s>
<s>
Similarly	O
,	O
in	O
the	O
formula	O
,	O
the	O
symbol	O
is	O
a	O
predicate	B-Algorithm
that	O
applies	O
to	O
the	O
individual	O
constants	O
and	O
.	O
</s>
<s>
In	O
the	O
semantics	O
of	O
logic	O
,	O
predicates	B-Algorithm
are	O
interpreted	O
as	O
relations	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
a	O
standard	O
semantics	O
for	O
first-order	O
logic	O
,	O
the	O
formula	O
would	O
be	O
true	O
on	O
an	O
interpretation	O
if	O
the	O
entities	O
denoted	O
by	O
and	O
stand	O
in	O
the	O
relation	B-Algorithm
denoted	O
by	O
.	O
</s>
<s>
Since	O
predicates	B-Algorithm
are	O
non-logical	O
symbols	O
,	O
they	O
can	O
denote	O
different	O
relations	O
depending	O
on	O
the	O
interpretation	O
given	O
to	O
them	O
.	O
</s>
<s>
While	O
first-order	O
logic	O
only	O
includes	O
predicates	B-Algorithm
that	O
apply	O
to	O
individual	O
constants	O
,	O
other	O
logics	O
may	O
allow	O
predicates	B-Algorithm
that	O
apply	O
to	O
other	O
predicates	B-Algorithm
.	O
</s>
<s>
A	O
predicate	B-Algorithm
is	O
a	O
statement	O
or	O
mathematical	O
assertion	O
that	O
contains	O
variables	O
,	O
sometimes	O
referred	O
to	O
as	O
predicate	B-Algorithm
variables	I-Algorithm
,	O
and	O
may	O
be	O
true	O
or	O
false	O
depending	O
on	O
those	O
variables’	O
value	O
or	O
values	O
.	O
</s>
<s>
In	O
propositional	O
logic	O
,	O
atomic	B-Algorithm
formulas	I-Algorithm
are	O
sometimes	O
regarded	O
as	O
zero-place	O
predicates	B-Algorithm
.	O
</s>
<s>
0-arity	O
)	O
predicates	B-Algorithm
.	O
</s>
<s>
In	O
first-order	O
logic	O
,	O
a	O
predicate	B-Algorithm
forms	O
an	O
atomic	B-Algorithm
formula	I-Algorithm
when	O
applied	O
to	O
an	O
appropriate	O
number	O
of	O
terms	O
.	O
</s>
<s>
In	O
set	O
theory	O
with	O
the	O
law	O
of	O
excluded	O
middle	O
,	O
predicates	B-Algorithm
are	O
understood	O
to	O
be	O
characteristic	O
functions	O
or	O
set	O
indicator	O
functions	O
(	O
i.e.	O
,	O
functions	O
from	O
a	O
set	O
element	O
to	O
a	O
truth	O
value	O
)	O
.	O
</s>
<s>
Set-builder	B-Language
notation	I-Language
makes	O
use	O
of	O
predicates	B-Algorithm
to	O
define	O
sets	O
.	O
</s>
<s>
In	O
autoepistemic	B-Application
logic	I-Application
,	O
which	O
rejects	O
the	O
law	O
of	O
excluded	O
middle	O
,	O
predicates	B-Algorithm
may	O
be	O
true	O
,	O
false	O
,	O
or	O
simply	O
unknown	O
.	O
</s>
<s>
In	O
particular	O
,	O
a	O
given	O
collection	O
of	O
facts	O
may	O
be	O
insufficient	O
to	O
determine	O
the	O
truth	O
or	O
falsehood	O
of	O
a	O
predicate	B-Algorithm
.	O
</s>
<s>
In	O
fuzzy	O
logic	O
,	O
the	O
strict	O
true/false	O
valuation	O
of	O
the	O
predicate	B-Algorithm
is	O
replaced	O
by	O
a	O
quantity	O
interpreted	O
as	O
the	O
degree	O
of	O
truth	O
.	O
</s>
