<s>
The	O
closed-world	B-Application
assumption	I-Application
(	O
CWA	O
)	O
,	O
in	O
a	O
formal	O
system	O
of	O
logic	O
used	O
for	O
knowledge	O
representation	O
,	O
is	O
the	O
presumption	O
that	O
a	O
statement	O
that	O
is	O
true	O
is	O
also	O
known	O
to	O
be	O
true	O
.	O
</s>
<s>
The	O
opposite	O
of	O
the	O
closed-world	B-Application
assumption	I-Application
is	O
the	O
open-world	B-Application
assumption	I-Application
(	O
OWA	O
)	O
,	O
stating	O
that	O
lack	O
of	O
knowledge	O
does	O
not	O
imply	O
falsity	O
.	O
</s>
<s>
Negation	B-Application
as	I-Application
failure	I-Application
is	O
related	O
to	O
the	O
closed-world	B-Application
assumption	I-Application
,	O
as	O
it	O
amounts	O
to	O
believing	O
false	O
every	O
predicate	O
that	O
cannot	O
be	O
proved	O
to	O
be	O
true	O
.	O
</s>
<s>
In	O
the	O
context	O
of	O
knowledge	O
management	O
,	O
the	O
closed-world	B-Application
assumption	I-Application
is	O
used	O
in	O
at	O
least	O
two	O
situations	O
:	O
(	O
1	O
)	O
when	O
the	O
knowledge	O
base	O
is	O
known	O
to	O
be	O
complete	O
(	O
e.g.	O
,	O
a	O
corporate	O
database	O
containing	O
records	O
for	O
every	O
employee	O
)	O
,	O
and	O
(	O
2	O
)	O
when	O
the	O
knowledge	O
base	O
is	O
known	O
to	O
be	O
incomplete	O
but	O
a	O
"	O
best	O
"	O
definite	O
answer	O
must	O
be	O
derived	O
from	O
incomplete	O
information	O
.	O
</s>
<s>
In	O
the	O
closed-world	B-Application
assumption	I-Application
,	O
the	O
table	O
is	O
assumed	O
to	O
be	O
complete	O
(	O
it	O
lists	O
all	O
editor-article	O
relationships	O
)	O
,	O
and	O
Sarah	O
Johnson	O
is	O
the	O
only	O
editor	O
who	O
has	O
not	O
edited	O
the	O
article	O
on	O
Formal	O
Logic	O
.	O
</s>
<s>
In	O
contrast	O
,	O
with	O
the	O
open-world	B-Application
assumption	I-Application
the	O
table	O
is	O
not	O
assumed	O
to	O
contain	O
all	O
editor-article	O
tuples	O
,	O
and	O
the	O
answer	O
to	O
who	O
has	O
not	O
edited	O
the	O
Formal	O
Logic	O
article	O
is	O
unknown	O
.	O
</s>
<s>
The	O
first	O
formalization	O
of	O
the	O
closed-world	B-Application
assumption	I-Application
in	O
formal	O
logic	O
consists	O
in	O
adding	O
to	O
the	O
knowledge	O
base	O
the	O
negation	O
of	O
the	O
literals	O
that	O
are	O
not	O
currently	O
entailed	O
by	O
it	O
.	O
</s>
<s>
The	O
result	O
of	O
this	O
addition	O
is	O
always	O
consistent	O
if	O
the	O
knowledge	O
base	O
is	O
in	O
Horn	B-Application
form	I-Application
,	O
but	O
is	O
not	O
guaranteed	O
to	O
be	O
consistent	O
otherwise	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
this	O
formalization	O
of	O
the	O
closed-world	B-Application
assumption	I-Application
sometimes	O
turns	O
a	O
consistent	O
knowledge	O
base	O
into	O
an	O
inconsistent	O
one	O
.	O
</s>
<s>
The	O
closed-world	B-Application
assumption	I-Application
does	O
not	O
introduce	O
an	O
inconsistency	O
on	O
a	O
knowledge	O
base	O
exactly	O
when	O
the	O
intersection	O
of	O
all	O
Herbrand	O
models	O
of	O
is	O
also	O
a	O
model	O
of	O
;	O
in	O
the	O
propositional	O
case	O
,	O
this	O
condition	O
is	O
equivalent	O
to	O
having	O
a	O
single	O
minimal	O
model	O
,	O
where	O
a	O
model	O
is	O
minimal	O
if	O
no	O
other	O
model	O
has	O
a	O
subset	O
of	O
variables	O
assigned	O
to	O
true	O
.	O
</s>
<s>
In	O
all	O
cases	O
,	O
the	O
formalization	O
of	O
the	O
closed-world	B-Application
assumption	I-Application
is	O
based	O
on	O
adding	O
to	O
the	O
negation	O
of	O
the	O
formulae	O
that	O
are	O
“	O
free	O
for	O
negation	O
”	O
for	O
,	O
i.e.	O
,	O
the	O
formulae	O
that	O
can	O
be	O
assumed	O
to	O
be	O
false	O
.	O
</s>
<s>
The	O
set	O
of	O
formulae	O
that	O
are	O
free	O
for	O
negation	O
in	O
can	O
be	O
defined	O
in	O
different	O
ways	O
,	O
leading	O
to	O
different	O
formalizations	O
of	O
the	O
closed-world	B-Application
assumption	I-Application
.	O
</s>
<s>
CWA	O
(	O
closed-world	B-Application
assumption	I-Application
)	O
is	O
a	O
positive	O
literal	O
not	O
entailed	O
by	O
;	O
</s>
<s>
The	O
ECWA	O
and	O
the	O
formalism	O
of	O
circumscription	B-Application
coincide	O
on	O
propositional	O
theories	O
.	O
</s>
<s>
The	O
complexity	O
of	O
query	O
answering	O
(	O
checking	O
whether	O
a	O
formula	O
is	O
entailed	O
by	O
another	O
one	O
under	O
the	O
closed-world	B-Application
assumption	I-Application
)	O
is	O
typically	O
in	O
the	O
second	O
level	O
of	O
the	O
polynomial	O
hierarchy	O
for	O
general	O
formulae	O
,	O
and	O
ranges	O
from	O
P	O
to	O
coNP	O
for	O
Horn	B-Application
formulae	I-Application
.	O
</s>
<s>
Checking	O
whether	O
the	O
original	O
closed-world	B-Application
assumption	I-Application
introduces	O
an	O
inconsistency	O
requires	O
at	O
most	O
a	O
logarithmic	O
number	O
of	O
calls	O
to	O
an	O
NP	O
oracle	O
;	O
however	O
,	O
the	O
exact	O
complexity	O
of	O
this	O
problem	O
is	O
not	O
currently	O
known	O
.	O
</s>
