<s>
Version	B-General_Concept
space	I-General_Concept
learning	I-General_Concept
is	O
a	O
logical	B-General_Concept
approach	O
to	O
machine	O
learning	O
,	O
specifically	O
binary	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
Version	B-General_Concept
space	I-General_Concept
learning	I-General_Concept
algorithms	O
search	O
a	O
predefined	O
space	O
of	O
hypotheses	O
,	O
viewed	O
as	O
a	O
set	O
of	O
logical	B-General_Concept
sentences	O
.	O
</s>
<s>
A	O
version	B-General_Concept
space	I-General_Concept
learning	I-General_Concept
algorithm	O
is	O
presented	O
with	O
examples	O
,	O
which	O
it	O
will	O
use	O
to	O
restrict	O
its	O
hypothesis	O
space	O
;	O
for	O
each	O
example	O
,	O
the	O
hypotheses	O
that	O
are	O
inconsistent	B-General_Concept
with	O
are	O
removed	O
from	O
the	O
space	O
.	O
</s>
<s>
This	O
iterative	O
refining	O
of	O
the	O
hypothesis	O
space	O
is	O
called	O
the	O
candidate	B-General_Concept
elimination	I-General_Concept
algorithm	O
,	O
the	O
hypothesis	O
space	O
maintained	O
inside	O
the	O
algorithm	O
its	O
version	B-General_Concept
space	I-General_Concept
.	O
</s>
<s>
In	O
settings	O
where	O
there	O
is	O
a	O
generality-ordering	O
on	O
hypotheses	O
,	O
it	O
is	O
possible	O
to	O
represent	O
the	O
version	B-General_Concept
space	I-General_Concept
by	O
two	O
sets	O
of	O
hypotheses	O
:	O
(	O
1	O
)	O
the	O
most	O
specific	O
consistent	O
hypotheses	O
,	O
and	O
(	O
2	O
)	O
the	O
most	O
general	O
consistent	O
hypotheses	O
,	O
where	O
"	O
consistent	O
"	O
indicates	O
agreement	O
with	O
observed	O
data	O
.	O
</s>
<s>
The	O
most	O
specific	O
hypotheses	O
(	O
i.e.	O
,	O
the	O
specific	O
boundary	O
SB	O
)	O
cover	O
the	O
observed	O
positive	O
training	O
examples	O
,	O
and	O
as	O
little	O
of	O
the	O
remaining	O
feature	B-Algorithm
space	I-Algorithm
as	O
possible	O
.	O
</s>
<s>
These	O
hypotheses	O
,	O
if	O
reduced	O
any	O
further	O
,	O
exclude	O
a	O
positive	O
training	O
example	O
,	O
and	O
hence	O
become	O
inconsistent	B-General_Concept
.	O
</s>
<s>
The	O
most	O
general	O
hypotheses	O
(	O
i.e.	O
,	O
the	O
general	O
boundary	O
GB	O
)	O
cover	O
the	O
observed	O
positive	O
training	O
examples	O
,	O
but	O
also	O
cover	O
as	O
much	O
of	O
the	O
remaining	O
feature	B-Algorithm
space	I-Algorithm
without	O
including	O
any	O
negative	O
training	O
examples	O
.	O
</s>
<s>
These	O
,	O
if	O
enlarged	O
any	O
further	O
,	O
include	O
a	O
negative	O
training	O
example	O
,	O
and	O
hence	O
become	O
inconsistent	B-General_Concept
.	O
</s>
<s>
Thus	O
,	O
during	O
learning	O
,	O
the	O
version	B-General_Concept
space	I-General_Concept
(	O
which	O
itself	O
is	O
a	O
set	O
–	O
possibly	O
infinite	O
–	O
containing	O
all	O
consistent	O
hypotheses	O
)	O
can	O
be	O
represented	O
by	O
just	O
its	O
lower	O
and	O
upper	O
bounds	O
(	O
maximally	O
general	O
and	O
maximally	O
specific	O
hypothesis	O
sets	O
)	O
,	O
and	O
learning	O
operations	O
can	O
be	O
performed	O
just	O
on	O
these	O
representative	O
sets	O
.	O
</s>
<s>
The	O
notion	O
of	O
version	B-General_Concept
spaces	I-General_Concept
was	O
introduced	O
by	O
Mitchell	O
in	O
the	O
early	O
1980s	O
as	O
a	O
framework	O
for	O
understanding	O
the	O
basic	O
problem	O
of	O
supervised	O
learning	O
within	O
the	O
context	O
of	O
solution	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
Although	O
the	O
basic	O
"	O
candidate	B-General_Concept
elimination	I-General_Concept
"	O
search	O
method	O
that	O
accompanies	O
the	O
version	B-General_Concept
space	I-General_Concept
framework	O
is	O
not	O
a	O
popular	O
learning	O
algorithm	O
,	O
there	O
are	O
some	O
practical	O
implementations	O
that	O
have	O
been	O
developed	O
(	O
e.g.	O
,	O
Sverdlik	O
&	O
Reynolds	O
1992	O
,	O
Hong	O
&	O
Tsang	O
1997	O
,	O
Dubois	O
&	O
Quafafou	O
2002	O
)	O
.	O
</s>
<s>
A	O
major	O
drawback	O
of	O
version	B-General_Concept
space	I-General_Concept
learning	I-General_Concept
is	O
its	O
inability	O
to	O
deal	O
with	O
noise	O
:	O
any	O
pair	O
of	O
inconsistent	B-General_Concept
examples	O
can	O
cause	O
the	O
version	B-General_Concept
space	I-General_Concept
to	O
collapse	O
,	O
i.e.	O
,	O
become	O
empty	O
,	O
so	O
that	O
classification	O
becomes	O
impossible	O
.	O
</s>
<s>
One	O
solution	O
of	O
this	O
problem	O
is	O
proposed	O
by	O
Dubois	O
and	O
Quafafou	O
that	O
proposed	O
the	O
Rough	O
Version	B-General_Concept
Space	I-General_Concept
,	O
where	O
rough	O
sets	O
based	O
approximations	O
are	O
used	O
to	O
learn	O
certain	O
and	O
possible	O
hypothesis	O
in	O
the	O
presence	O
of	O
inconsistent	B-General_Concept
data	O
.	O
</s>
