<s>
The	O
situation	B-Application
calculus	I-Application
is	O
a	O
logic	O
formalism	O
designed	O
for	O
representing	O
and	O
reasoning	O
about	O
dynamical	O
domains	O
.	O
</s>
<s>
It	O
is	O
followed	O
by	O
sections	O
about	O
McCarthy	O
's	O
1986	O
version	O
and	O
a	O
logic	B-Language
programming	I-Language
formulation	O
.	O
</s>
<s>
The	O
situation	B-Application
calculus	I-Application
represents	O
changing	O
scenarios	O
as	O
a	O
set	O
of	O
first-order	O
logic	O
formulae	O
.	O
</s>
<s>
The	O
main	O
elements	O
of	O
the	O
situation	B-Application
calculus	I-Application
are	O
the	O
actions	O
,	O
fluents	O
and	O
the	O
situations	O
.	O
</s>
<s>
The	O
situation	B-Application
calculus	I-Application
is	O
based	O
on	O
a	O
sorted	O
domain	O
with	O
three	O
sorts	O
:	O
actions	O
,	O
situations	O
,	O
and	O
objects	O
,	O
where	O
the	O
objects	O
include	O
everything	O
that	O
is	O
not	O
an	O
action	O
or	O
a	O
situation	O
.	O
</s>
<s>
In	O
the	O
situation	B-Application
calculus	I-Application
,	O
a	O
dynamic	O
world	O
is	O
modeled	O
as	O
progressing	O
through	O
a	O
series	O
of	O
situations	O
as	O
a	O
result	O
of	O
various	O
actions	O
being	O
performed	O
within	O
the	O
world	O
.	O
</s>
<s>
In	O
the	O
Reiter	O
version	O
of	O
the	O
situation	B-Application
calculus	I-Application
described	O
here	O
,	O
a	O
situation	O
does	O
not	O
represent	O
a	O
state	O
,	O
contrarily	O
to	O
the	O
literal	O
meaning	O
of	O
the	O
term	O
and	O
contrarily	O
to	O
the	O
original	O
definition	O
by	O
McCarthy	O
and	O
Hayes	O
.	O
</s>
<s>
While	O
this	O
formula	O
correctly	O
describes	O
the	O
effect	O
of	O
the	O
actions	O
,	O
it	O
is	O
not	O
sufficient	O
to	O
correctly	O
describe	O
the	O
action	O
in	O
logic	O
,	O
because	O
of	O
the	O
frame	B-Application
problem	I-Application
.	O
</s>
<s>
The	O
need	O
to	O
specify	O
frame	O
axioms	O
has	O
long	O
been	O
recognised	O
as	O
a	O
problem	O
in	O
axiomatizing	O
dynamic	O
worlds	O
,	O
and	O
is	O
known	O
as	O
the	O
frame	B-Application
problem	I-Application
.	O
</s>
<s>
The	O
successor	O
state	O
axioms	O
"	O
solve	O
"	O
the	O
frame	B-Application
problem	I-Application
in	O
the	O
situation	B-Application
calculus	I-Application
.	O
</s>
<s>
The	O
foundational	O
axioms	O
of	O
the	O
situation	B-Application
calculus	I-Application
formalize	O
the	O
idea	O
that	O
situations	O
are	O
histories	O
by	O
having	O
.	O
</s>
<s>
Regression	O
is	O
a	O
mechanism	O
for	O
proving	O
consequences	O
in	O
the	O
situation	B-Application
calculus	I-Application
.	O
</s>
<s>
GOLOG	O
is	O
a	O
logic	B-Language
programming	I-Language
language	I-Language
based	O
on	O
the	O
situation	B-Application
calculus	I-Application
.	O
</s>
<s>
The	O
main	O
difference	O
between	O
the	O
original	O
situation	B-Application
calculus	I-Application
by	O
McCarthy	O
and	O
Hayes	O
and	O
the	O
one	O
in	O
use	O
today	O
is	O
the	O
interpretation	O
of	O
situations	O
.	O
</s>
<s>
This	O
is	O
also	O
different	O
from	O
the	O
approach	O
that	O
is	O
taken	O
by	O
the	O
fluent	B-Application
calculus	I-Application
,	O
where	O
a	O
state	O
can	O
be	O
a	O
collection	O
of	O
known	O
facts	O
,	O
that	O
is	O
,	O
a	O
possibly	O
incomplete	O
description	O
of	O
the	O
universe	O
.	O
</s>
<s>
In	O
the	O
original	O
version	O
of	O
the	O
situation	B-Application
calculus	I-Application
,	O
fluents	O
are	O
not	O
reified	O
.	O
</s>
<s>
In	O
the	O
1986	O
version	O
of	O
the	O
situation	B-Application
calculus	I-Application
by	O
McCarthy	O
,	O
functional	O
fluents	O
are	O
used	O
.	O
</s>
<s>
In	O
the	O
original	O
formulation	O
of	O
the	O
situation	B-Application
calculus	I-Application
,	O
the	O
initial	O
situation	O
,	O
later	O
denoted	O
by	O
,	O
is	O
not	O
explicitly	O
identified	O
.	O
</s>
<s>
The	O
initial	O
situation	O
is	O
instead	O
necessary	O
if	O
,	O
like	O
in	O
the	O
modern	O
situation	B-Application
calculus	I-Application
,	O
a	O
situation	O
is	O
taken	O
to	O
be	O
a	O
history	O
of	O
actions	O
,	O
as	O
the	O
initial	O
situation	O
represents	O
the	O
empty	O
sequence	O
of	O
actions	O
.	O
</s>
<s>
The	O
version	O
of	O
the	O
situation	B-Application
calculus	I-Application
introduced	O
by	O
McCarthy	O
in	O
1986	O
differs	O
to	O
the	O
original	O
one	O
for	O
the	O
use	O
of	O
functional	O
fluents	O
(	O
e.g.	O
,	O
is	O
a	O
term	O
representing	O
the	O
position	O
of	O
in	O
the	O
situation	O
)	O
and	O
for	O
an	O
attempt	O
to	O
use	O
circumscription	B-Application
to	O
replace	O
the	O
frame	O
axioms	O
.	O
</s>
<s>
Kowalski	O
1979	O
,	O
Apt	O
and	O
Bezem	O
1990	O
,	O
Shanahan	O
1997	O
)	O
to	O
write	O
the	O
situation	B-Application
calculus	I-Application
as	O
a	O
logic	B-Language
program	I-Language
:	O
</s>
<s>
The	O
other	O
half	O
is	O
implicit	O
in	O
the	O
completion	O
of	O
the	O
program	O
,	O
in	O
which	O
negation	O
is	O
interpreted	O
as	O
negation	B-Application
as	I-Application
failure	I-Application
.	O
</s>
<s>
Backward	O
reasoning	O
as	O
in	O
SLD	B-Application
resolution	I-Application
,	O
which	O
is	O
the	O
usual	O
mechanism	O
used	O
to	O
execute	O
logic	B-Language
programs	I-Language
,	O
implements	O
regression	O
implicitly	O
.	O
</s>
