<s>
The	O
autoepistemic	B-Application
logic	I-Application
is	O
a	O
formal	O
logic	O
for	O
the	O
representation	O
and	O
reasoning	O
of	O
knowledge	O
about	O
knowledge	O
.	O
</s>
<s>
While	O
propositional	O
logic	O
can	O
only	O
express	O
facts	O
,	O
autoepistemic	B-Application
logic	I-Application
can	O
express	O
knowledge	O
and	O
lack	O
of	O
knowledge	O
about	O
facts	O
.	O
</s>
<s>
The	O
stable	B-Application
model	I-Application
semantics	I-Application
,	O
which	O
is	O
used	O
to	O
give	O
a	O
semantics	O
to	O
logic	B-Language
programming	I-Language
with	O
negation	B-Application
as	I-Application
failure	I-Application
,	O
can	O
be	O
seen	O
as	O
a	O
simplified	O
form	O
of	O
autoepistemic	B-Application
logic	I-Application
.	O
</s>
<s>
The	O
syntax	B-Application
of	O
autoepistemic	B-Application
logic	I-Application
extends	O
that	O
of	O
propositional	O
logic	O
by	O
a	O
modal	O
operator	O
indicating	O
knowledge	O
:	O
if	O
is	O
a	O
formula	O
,	O
indicates	O
that	O
is	O
known	O
.	O
</s>
<s>
This	O
syntax	B-Application
is	O
used	O
for	O
allowing	O
reasoning	O
based	O
on	O
knowledge	O
of	O
facts	O
.	O
</s>
<s>
This	O
is	O
a	O
form	O
of	O
negation	B-Application
as	I-Application
failure	I-Application
.	O
</s>
<s>
The	O
semantics	O
of	O
autoepistemic	B-Application
logic	I-Application
is	O
based	O
on	O
the	O
expansions	O
of	O
a	O
theory	O
,	O
which	O
have	O
a	O
role	O
similar	O
to	O
models	O
in	O
propositional	O
logic	O
.	O
</s>
<s>
Thus	O
,	O
autoepistemic	B-Application
logic	I-Application
extends	O
S5	O
;	O
the	O
extension	O
is	O
proper	O
,	O
since	O
and	O
are	O
tautologies	O
of	O
autoepistemic	B-Application
logic	I-Application
,	O
but	O
not	O
of	O
S5	O
.	O
</s>
<s>
Strongly	O
grounded	O
variants	O
of	O
autoepistemic	B-Application
logic	I-Application
exist	O
.	O
</s>
