<s>
In	O
logic	O
,	O
the	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
(	O
also	O
called	O
monadic	B-Application
first-order	I-Application
logic	I-Application
)	O
is	O
the	O
fragment	O
of	O
first-order	O
logic	O
in	O
which	O
all	O
relation	B-Algorithm
symbols	O
in	O
the	O
signature	O
are	O
monadic	O
(	O
that	O
is	O
,	O
they	O
take	O
only	O
one	O
argument	O
)	O
,	O
and	O
there	O
are	O
no	O
function	O
symbols	O
.	O
</s>
<s>
All	O
atomic	B-Algorithm
formulas	I-Algorithm
are	O
thus	O
of	O
the	O
form	O
,	O
where	O
is	O
a	O
relation	B-Algorithm
symbol	O
and	O
is	O
a	O
variable	O
.	O
</s>
<s>
Monadic	B-Application
predicate	I-Application
calculus	I-Application
can	O
be	O
contrasted	O
with	O
polyadic	O
predicate	O
calculus	O
,	O
which	O
allows	O
relation	B-Algorithm
symbols	O
that	O
take	O
two	O
or	O
more	O
arguments	O
.	O
</s>
<s>
The	O
absence	O
of	O
polyadic	B-Algorithm
relation	I-Algorithm
symbols	O
severely	O
restricts	O
what	O
can	O
be	O
expressed	O
in	O
the	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
.	O
</s>
<s>
It	O
is	O
so	O
weak	O
that	O
,	O
unlike	O
the	O
full	O
predicate	O
calculus	O
,	O
it	O
is	O
decidable	O
—	O
there	O
is	O
a	O
decision	O
procedure	O
that	O
determines	O
whether	O
a	O
given	O
formula	O
of	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
is	O
logically	O
valid	O
(	O
true	O
for	O
all	O
nonempty	O
domains	O
)	O
.	O
</s>
<s>
Adding	O
a	O
single	O
binary	O
relation	B-Algorithm
symbol	O
to	O
monadic	B-Application
logic	I-Application
,	O
however	O
,	O
results	O
in	O
an	O
undecidable	O
logic	O
.	O
</s>
<s>
The	O
need	O
to	O
go	O
beyond	O
monadic	B-Application
logic	I-Application
was	O
not	O
appreciated	O
until	O
the	O
work	O
on	O
the	O
logic	O
of	O
relations	O
,	O
by	O
Augustus	O
De	O
Morgan	O
and	O
Charles	O
Sanders	O
Peirce	O
in	O
the	O
nineteenth	O
century	O
,	O
and	O
by	O
Frege	O
in	O
his	O
1879	O
Begriffsschrifft	O
.	O
</s>
<s>
Inferences	O
in	O
term	O
logic	O
can	O
all	O
be	O
represented	O
in	O
the	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
.	O
</s>
<s>
Conversely	O
,	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
is	O
not	O
significantly	O
more	O
expressive	O
than	O
term	O
logic	O
.	O
</s>
<s>
Taking	O
propositional	O
logic	O
as	O
given	O
,	O
every	O
formula	O
in	O
the	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
expresses	O
something	O
that	O
can	O
likewise	O
be	O
formulated	O
in	O
term	O
logic	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
a	O
modern	O
view	O
of	O
the	O
problem	O
of	O
multiple	O
generality	O
in	O
traditional	O
logic	O
concludes	O
that	O
quantifiers	B-Language
cannot	O
nest	O
usefully	O
if	O
there	O
are	O
no	O
polyadic	O
predicates	O
to	O
relate	O
the	O
bound	O
variables	O
.	O
</s>
<s>
The	O
formal	O
system	O
described	O
above	O
is	O
sometimes	O
called	O
the	O
pure	O
monadic	B-Application
predicate	I-Application
calculus	I-Application
,	O
where	O
"	O
pure	O
"	O
signifies	O
the	O
absence	O
of	O
function	O
letters	O
.	O
</s>
<s>
Monadic	O
second-order	O
logic	O
allows	O
predicates	O
of	O
higher	O
arity	O
in	O
formulas	O
,	O
but	O
restricts	O
second-order	O
quantification	B-Language
to	O
unary	O
predicates	O
,	O
i.e.	O
</s>
