<s>
The	O
B	B-Application
,	I-Application
C	I-Application
,	I-Application
K	I-Application
,	I-Application
W	I-Application
system	I-Application
is	O
a	O
variant	O
of	O
combinatory	B-Application
logic	I-Application
that	O
takes	O
as	O
primitive	O
the	O
combinators	B-Application
B	O
,	O
C	O
,	O
K	O
,	O
and	O
W	O
.	O
This	O
system	O
was	O
discovered	O
by	O
Haskell	O
Curry	O
in	O
his	O
doctoral	O
thesis	O
Grundlagen	O
der	O
kombinatorischen	O
Logik	O
,	O
whose	O
results	O
are	O
set	O
out	O
in	O
Curry	O
(	O
1930	O
)	O
.	O
</s>
<s>
The	O
combinators	B-Application
are	O
defined	O
as	O
follows	O
:	O
</s>
<s>
B	O
x	O
y	O
is	O
the	O
composition	B-Application
of	O
x	O
and	O
y	O
;	O
</s>
<s>
In	O
recent	O
decades	O
,	O
the	O
SKI	B-Application
combinator	I-Application
calculus	I-Application
,	O
with	O
only	O
two	O
primitive	O
combinators	B-Application
,	O
K	O
and	O
S	O
,	O
has	O
become	O
the	O
canonical	O
approach	O
to	O
combinatory	B-Application
logic	I-Application
.	O
</s>
<s>
Also	O
of	O
note	O
,	O
Y	O
combinator	B-Application
has	O
a	O
short	O
expression	O
in	O
this	O
system	O
,	O
as	O
Y	O
=	O
BU(CBU )	O
,	O
where	O
U	O
=	O
WI	O
=	O
SII	O
is	O
the	O
self-application	O
combinator	B-Application
.	O
</s>
<s>
The	O
combinators	B-Application
B	O
,	O
C	O
,	O
K	O
and	O
W	O
correspond	O
to	O
four	O
well-known	O
axioms	O
of	O
sentential	O
logic	O
:	O
</s>
<s>
In	O
order	O
for	O
combinatory	B-Application
logic	I-Application
to	O
have	O
as	O
a	O
model	O
:	O
</s>
