<s>
In	O
artificial	B-Application
intelligence	I-Application
,	O
the	O
frame	B-Application
problem	I-Application
describes	O
an	O
issue	O
with	O
using	O
first-order	O
logic	O
(	O
FOL	O
)	O
to	O
express	O
facts	O
about	O
a	O
robot	O
in	O
the	O
world	O
.	O
</s>
<s>
Representing	O
the	O
state	O
of	O
a	O
robot	O
with	O
traditional	O
FOL	O
requires	O
the	O
use	O
of	O
many	O
axioms	B-Algorithm
that	O
simply	O
imply	O
that	O
things	O
in	O
the	O
environment	O
do	O
not	O
change	O
arbitrarily	O
.	O
</s>
<s>
For	O
example	O
,	O
Hayes	O
describes	O
a	O
"	O
block	B-General_Concept
world	I-General_Concept
"	O
with	O
rules	O
about	O
stacking	O
blocks	O
together	O
.	O
</s>
<s>
In	O
a	O
FOL	O
system	O
,	O
additional	O
axioms	B-Algorithm
are	O
required	O
to	O
make	O
inferences	O
about	O
the	O
environment	O
(	O
for	O
example	O
,	O
that	O
a	O
block	O
cannot	O
change	O
position	O
unless	O
it	O
is	O
physically	O
moved	O
)	O
.	O
</s>
<s>
The	O
frame	B-Application
problem	I-Application
is	O
the	O
problem	O
of	O
finding	O
adequate	O
collections	O
of	O
axioms	B-Algorithm
for	O
a	O
viable	O
description	O
of	O
a	O
robot	O
environment	O
.	O
</s>
<s>
John	O
McCarthy	O
and	O
Patrick	O
J	O
.	O
Hayes	O
defined	O
this	O
problem	O
in	O
their	O
1969	O
article	O
,	O
Some	O
Philosophical	O
Problems	O
from	O
the	O
Standpoint	O
of	O
Artificial	B-Application
Intelligence	I-Application
.	I-Application
</s>
<s>
In	O
this	O
paper	O
,	O
and	O
many	O
that	O
came	O
after	O
,	O
the	O
formal	O
mathematical	O
problem	O
was	O
a	O
starting	O
point	O
for	O
more	O
general	O
discussions	O
of	O
the	O
difficulty	O
of	O
knowledge	O
representation	O
for	O
artificial	B-Application
intelligence	I-Application
.	I-Application
</s>
<s>
The	O
frame	B-Application
problem	I-Application
occurs	O
even	O
in	O
very	O
simple	O
domains	O
.	O
</s>
<s>
If	O
these	O
conditions	O
can	O
change	O
,	O
they	O
are	O
better	O
represented	O
by	O
two	O
predicates	B-Algorithm
and	O
that	O
depend	O
on	O
time	O
;	O
such	O
predicates	B-Algorithm
are	O
called	O
fluents	O
.	O
</s>
<s>
In	O
practice	O
,	O
one	O
would	O
have	O
a	O
predicate	B-Algorithm
for	O
specifying	O
when	O
an	O
action	O
is	O
executed	O
and	O
a	O
rule	O
for	O
specifying	O
the	O
effects	O
of	O
actions	O
.	O
</s>
<s>
The	O
article	O
on	O
the	O
situation	B-Application
calculus	I-Application
gives	O
more	O
details	O
.	O
</s>
<s>
The	O
frame	B-Application
problem	I-Application
is	O
that	O
specifying	O
only	O
which	O
conditions	O
are	O
changed	O
by	O
the	O
actions	O
does	O
not	O
entail	O
that	O
all	O
other	O
conditions	O
are	O
not	O
changed	O
.	O
</s>
<s>
This	O
problem	O
can	O
be	O
solved	O
by	O
adding	O
the	O
so-called	O
“	O
frame	O
axioms	B-Algorithm
”	O
,	O
which	O
explicitly	O
specify	O
that	O
all	O
conditions	O
not	O
affected	O
by	O
actions	O
are	O
not	O
changed	O
while	O
executing	O
that	O
action	O
.	O
</s>
<s>
For	O
example	O
,	O
since	O
the	O
action	O
executed	O
at	O
time	O
0	O
is	O
that	O
of	O
opening	O
the	O
door	O
,	O
a	O
frame	O
axiom	B-Algorithm
would	O
state	O
that	O
the	O
status	O
of	O
the	O
light	O
does	O
not	O
change	O
from	O
time	O
0	O
to	O
time	O
1	O
:	O
</s>
<s>
The	O
frame	B-Application
problem	I-Application
is	O
that	O
one	O
such	O
frame	O
axiom	B-Algorithm
is	O
necessary	O
for	O
every	O
pair	O
of	O
action	O
and	O
condition	O
such	O
that	O
the	O
action	O
does	O
not	O
affect	O
the	O
condition	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
the	O
problem	O
is	O
that	O
of	O
formalizing	O
a	O
dynamical	O
domain	O
without	O
explicitly	O
specifying	O
the	O
frame	O
axioms	B-Algorithm
.	O
</s>
<s>
The	O
solution	O
proposed	O
by	O
McCarthy	O
to	O
solve	O
this	O
problem	O
involves	O
assuming	O
that	O
a	O
minimal	O
amount	O
of	O
condition	O
changes	O
have	O
occurred	O
;	O
this	O
solution	O
is	O
formalized	O
using	O
the	O
framework	O
of	O
circumscription	B-Application
.	O
</s>
<s>
Alternative	O
solutions	O
were	O
then	O
proposed	O
,	O
involving	O
predicate	B-Algorithm
completion	O
,	O
fluent	O
occlusion	O
,	O
successor	O
state	O
axioms	B-Algorithm
,	O
etc	O
.	O
</s>
<s>
By	O
the	O
end	O
of	O
the	O
1980s	O
,	O
the	O
frame	B-Application
problem	I-Application
as	O
defined	O
by	O
McCarthy	O
and	O
Hayes	O
was	O
solved	O
.	O
</s>
<s>
Even	O
after	O
that	O
,	O
however	O
,	O
the	O
term	O
“	O
frame	B-Application
problem	I-Application
”	O
was	O
still	O
used	O
,	O
in	O
part	O
to	O
refer	O
to	O
the	O
same	O
problem	O
but	O
under	O
different	O
settings	O
(	O
e.g.	O
,	O
concurrent	O
actions	O
)	O
,	O
and	O
in	O
part	O
to	O
refer	O
to	O
the	O
general	O
problem	O
of	O
representing	O
and	O
reasoning	O
with	O
dynamical	O
domains	O
.	O
</s>
<s>
The	O
following	O
solutions	O
depict	O
how	O
the	O
frame	B-Application
problem	I-Application
is	O
solved	O
in	O
various	O
formalisms	O
.	O
</s>
<s>
In	O
the	O
simplified	O
example	O
of	O
the	O
door	O
and	O
the	O
light	O
,	O
occlusion	O
can	O
be	O
formalized	O
by	O
two	O
predicates	B-Algorithm
and	O
.	O
</s>
<s>
The	O
rationale	O
is	O
that	O
a	O
condition	O
can	O
change	O
value	O
only	O
if	O
the	O
corresponding	O
occlusion	O
predicate	B-Algorithm
is	O
true	O
at	O
the	O
next	O
time	O
point	O
.	O
</s>
<s>
In	O
turn	O
,	O
the	O
occlusion	O
predicate	B-Algorithm
is	O
true	O
only	O
when	O
an	O
action	O
affecting	O
the	O
condition	O
is	O
executed	O
.	O
</s>
<s>
In	O
general	O
,	O
every	O
action	O
making	O
a	O
condition	O
true	O
or	O
false	O
also	O
makes	O
the	O
corresponding	O
occlusion	O
predicate	B-Algorithm
true	O
.	O
</s>
<s>
In	O
order	O
for	O
this	O
condition	O
to	O
work	O
,	O
occlusion	O
predicates	B-Algorithm
have	O
to	O
be	O
true	O
only	O
when	O
they	O
are	O
made	O
true	O
as	O
an	O
effect	O
of	O
an	O
action	O
.	O
</s>
<s>
This	O
can	O
be	O
achieved	O
either	O
by	O
circumscription	B-Application
or	O
by	O
predicate	B-Algorithm
completion	O
.	O
</s>
<s>
It	O
is	O
worth	O
noticing	O
that	O
occlusion	O
does	O
not	O
necessarily	O
imply	O
a	O
change	O
:	O
for	O
example	O
,	O
executing	O
the	O
action	O
of	O
opening	O
the	O
door	O
when	O
it	O
was	O
already	O
open	O
(	O
in	O
the	O
formalization	O
above	O
)	O
makes	O
the	O
predicate	B-Algorithm
true	O
and	O
makes	O
true	O
;	O
however	O
,	O
has	O
not	O
changed	O
value	O
,	O
as	O
it	O
was	O
true	O
already	O
.	O
</s>
<s>
This	O
encoding	O
is	O
similar	O
to	O
the	O
fluent	O
occlusion	O
solution	O
,	O
but	O
the	O
additional	O
predicates	B-Algorithm
denote	O
change	O
,	O
not	O
permission	O
to	O
change	O
.	O
</s>
<s>
For	O
example	O
,	O
represents	O
the	O
fact	O
that	O
the	O
predicate	B-Algorithm
will	O
change	O
from	O
time	O
to	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
a	O
predicate	B-Algorithm
changes	O
if	O
and	O
only	O
if	O
the	O
corresponding	O
change	O
predicate	B-Algorithm
is	O
true	O
.	O
</s>
<s>
The	O
last	O
two	O
conditions	O
state	O
that	O
a	O
condition	O
changes	O
value	O
at	O
time	O
if	O
and	O
only	O
if	O
the	O
corresponding	O
change	O
predicate	B-Algorithm
is	O
true	O
at	O
time	O
.	O
</s>
<s>
To	O
complete	O
the	O
solution	O
,	O
the	O
time	O
points	O
in	O
which	O
the	O
change	O
predicates	B-Algorithm
are	O
true	O
have	O
to	O
be	O
as	O
few	O
as	O
possible	O
,	O
and	O
this	O
can	O
be	O
done	O
by	O
applying	O
predicate	B-Algorithm
completion	O
to	O
the	O
rules	O
specifying	O
the	O
effects	O
of	O
actions	O
.	O
</s>
<s>
A	O
successor	O
state	O
axiom	B-Algorithm
is	O
a	O
formalization	O
in	O
logic	O
of	O
these	O
two	O
facts	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
there	O
is	O
an	O
axiom	B-Algorithm
for	O
every	O
condition	O
,	O
</s>
<s>
The	O
fluent	B-Application
calculus	I-Application
is	O
a	O
variant	O
of	O
the	O
situation	B-Application
calculus	I-Application
.	O
</s>
<s>
terms	O
,	O
rather	O
than	O
predicates	B-Algorithm
,	O
to	O
represent	O
the	O
states	O
.	O
</s>
<s>
The	O
difference	O
between	O
a	O
predicate	B-Algorithm
and	O
a	O
term	O
in	O
first-order	O
logic	O
is	O
that	O
a	O
term	O
is	O
a	O
representation	O
of	O
an	O
object	O
(	O
possibly	O
a	O
complex	O
object	O
composed	O
of	O
other	O
objects	O
)	O
,	O
while	O
a	O
predicate	B-Algorithm
represents	O
a	O
condition	O
that	O
can	O
be	O
true	O
or	O
false	O
when	O
evaluated	O
over	O
a	O
given	O
set	O
of	O
terms	O
.	O
</s>
<s>
In	O
the	O
fluent	B-Application
calculus	I-Application
,	O
each	O
possible	O
state	O
is	O
represented	O
by	O
a	O
term	O
obtained	O
by	O
composition	O
of	O
other	O
terms	O
,	O
each	O
one	O
representing	O
the	O
conditions	O
that	O
are	O
true	O
in	O
state	O
.	O
</s>
<s>
The	O
solution	O
to	O
the	O
frame	B-Application
problem	I-Application
given	O
in	O
the	O
fluent	B-Application
calculus	I-Application
is	O
to	O
specify	O
the	O
effects	O
of	O
actions	O
by	O
stating	O
how	O
a	O
term	O
representing	O
the	O
state	O
changes	O
when	O
the	O
action	O
is	O
executed	O
.	O
</s>
<s>
This	O
formula	O
works	O
provided	O
that	O
suitable	O
axioms	B-Algorithm
are	O
given	O
about	O
and	O
,	O
e.g.	O
,	O
a	O
term	O
containing	O
the	O
same	O
condition	O
twice	O
is	O
not	O
a	O
valid	O
state	O
(	O
for	O
example	O
,	O
is	O
always	O
false	O
for	O
every	O
and	O
)	O
.	O
</s>
<s>
The	O
event	B-Application
calculus	I-Application
uses	O
terms	O
for	O
representing	O
fluents	O
,	O
like	O
the	O
fluent	B-Application
calculus	I-Application
,	O
but	O
also	O
has	O
axioms	B-Algorithm
constraining	O
the	O
value	O
of	O
fluents	O
,	O
like	O
the	O
successor	O
state	O
axioms	B-Algorithm
.	O
</s>
<s>
In	O
the	O
event	B-Application
calculus	I-Application
,	O
inertia	O
is	O
enforced	O
by	O
formulae	O
stating	O
that	O
a	O
fluent	O
is	O
true	O
if	O
it	O
has	O
been	O
true	O
at	O
a	O
given	O
previous	O
time	O
point	O
and	O
no	O
action	O
changing	O
it	O
to	O
false	O
has	O
been	O
performed	O
in	O
the	O
meantime	O
.	O
</s>
<s>
Predicate	B-Algorithm
completion	O
is	O
still	O
needed	O
in	O
the	O
event	B-Application
calculus	I-Application
for	O
obtaining	O
that	O
a	O
fluent	O
is	O
made	O
true	O
only	O
if	O
an	O
action	O
making	O
it	O
true	O
has	O
been	O
performed	O
,	O
but	O
also	O
for	O
obtaining	O
that	O
an	O
action	O
had	O
been	O
performed	O
only	O
if	O
that	O
is	O
explicitly	O
stated	O
.	O
</s>
<s>
The	O
frame	B-Application
problem	I-Application
can	O
be	O
thought	O
of	O
as	O
the	O
problem	O
of	O
formalizing	O
the	O
principle	O
that	O
,	O
by	O
default	O
,	O
"	O
everything	O
is	O
presumed	O
to	O
remain	O
in	O
the	O
state	O
in	O
which	O
it	O
is	O
"	O
(	O
Leibniz	O
,	O
"	O
An	O
Introduction	O
to	O
a	O
Secret	O
Encyclopædia	O
"	O
,	O
c	O
.	O
1679	O
)	O
.	O
</s>
<s>
This	O
default	O
,	O
sometimes	O
called	O
the	O
commonsense	O
law	O
of	O
inertia	O
,	O
was	O
expressed	O
by	O
Raymond	O
Reiter	O
in	O
default	B-Application
logic	I-Application
:	O
</s>
<s>
Steve	O
Hanks	O
and	O
Drew	O
McDermott	O
argued	O
,	O
on	O
the	O
basis	O
of	O
their	O
Yale	O
shooting	O
example	O
,	O
that	O
this	O
solution	O
to	O
the	O
frame	B-Application
problem	I-Application
is	O
unsatisfactory	O
.	O
</s>
<s>
The	O
counterpart	O
of	O
the	O
default	B-Application
logic	I-Application
solution	O
in	O
the	O
language	O
of	O
answer	B-Application
set	I-Application
programming	I-Application
is	O
a	O
rule	O
with	O
strong	O
negation	O
:	O
</s>
<s>
There	O
appears	O
to	O
be	O
some	O
similarity	O
between	O
the	O
separation	O
logic	O
solution	O
to	O
the	O
frame	B-Application
problem	I-Application
and	O
that	O
of	O
the	O
fluent	B-Application
calculus	I-Application
mentioned	O
above	O
.	O
</s>
<s>
Action	B-Language
description	I-Language
languages	I-Language
elude	O
the	O
frame	B-Application
problem	I-Application
rather	O
than	O
solving	O
it	O
.	O
</s>
<s>
An	O
action	B-Language
description	I-Language
language	I-Language
is	O
a	O
formal	O
language	O
with	O
a	O
syntax	O
that	O
is	O
specific	O
for	O
describing	O
situations	O
and	O
actions	O
.	O
</s>
<s>
The	O
semantics	O
of	O
an	O
action	B-Language
description	I-Language
language	I-Language
depends	O
on	O
what	O
the	O
language	O
can	O
express	O
(	O
concurrent	O
actions	O
,	O
delayed	O
effects	O
,	O
etc	O
.	O
)	O
</s>
<s>
and	O
is	O
usually	O
based	O
on	O
transition	B-Application
systems	I-Application
.	O
</s>
<s>
Since	O
domains	O
are	O
expressed	O
in	O
these	O
languages	O
rather	O
than	O
directly	O
in	O
logic	O
,	O
the	O
frame	B-Application
problem	I-Application
only	O
arises	O
when	O
a	O
specification	O
given	O
in	O
an	O
action	O
description	O
logic	O
is	O
to	O
be	O
translated	O
into	O
logic	O
.	O
</s>
<s>
Typically	O
,	O
however	O
,	O
a	O
translation	O
is	O
given	O
from	O
these	O
languages	O
to	O
answer	B-Application
set	I-Application
programming	I-Application
rather	O
than	O
first-order	O
logic	O
.	O
</s>
