<s>
The	O
Planning	B-Application
Domain	I-Application
Definition	I-Application
Language	I-Application
(	O
PDDL	B-Application
)	O
is	O
an	O
attempt	O
to	O
standardize	O
Artificial	O
Intelligence	O
(	O
AI	O
)	O
planning	O
languages	O
.	O
</s>
<s>
It	O
was	O
first	O
developed	O
by	O
Drew	O
McDermott	O
and	O
his	O
colleagues	O
in	O
1998	O
(	O
inspired	O
by	O
STRIPS	B-Application
and	O
ADL	B-Language
among	O
others	O
)	O
mainly	O
to	O
make	O
the	O
1998/2000	O
possible	O
,	O
and	O
then	O
evolved	O
with	O
each	O
competition	O
.	O
</s>
<s>
The	O
standardization	O
provided	O
by	O
PDDL	B-Application
has	O
the	O
benefit	O
of	O
making	O
research	O
more	O
reusable	O
and	O
easily	O
comparable	O
,	O
though	O
at	O
the	O
cost	O
of	O
some	O
expressive	O
power	O
,	O
compared	O
to	O
domain-specific	O
systems	O
.	O
</s>
<s>
Thus	O
several	O
problem-descriptions	O
may	O
be	O
connected	O
to	O
the	O
same	O
domain-description	O
(	O
just	O
as	O
several	O
instances	O
may	O
exist	O
of	O
a	O
class	O
in	O
OOP	B-Language
(	O
Object	B-Language
Oriented	I-Language
Programming	I-Language
)	O
or	O
in	O
OWL	B-Language
(	O
Web	B-Language
Ontology	I-Language
Language	I-Language
)	O
for	O
example	O
)	O
.	O
</s>
<s>
Thus	O
a	O
domain	O
and	O
a	O
connecting	O
problem	O
description	O
forms	O
the	O
PDDL-model	O
of	O
a	O
planning-problem	O
,	O
and	O
eventually	O
this	O
is	O
the	O
input	O
of	O
a	O
planner	O
(	O
usually	O
domain-independent	O
AI	B-Application
planner	I-Application
)	O
software	O
,	O
which	O
aims	O
to	O
solve	O
the	O
given	O
planning-problem	O
via	O
some	O
appropriate	O
planning	B-Application
algorithm	I-Application
.	O
</s>
<s>
The	O
output	O
of	O
the	O
planner	O
is	O
not	O
specified	O
by	O
PDDL	B-Application
,	O
but	O
it	O
is	O
usually	O
a	O
totally	B-Application
or	I-Application
partially	I-Application
ordered	I-Application
plan	I-Application
(	O
a	O
sequence	O
of	O
actions	O
,	O
some	O
of	O
which	O
may	O
be	O
executed	O
even	O
in	O
parallel	O
sometimes	O
)	O
.	O
</s>
<s>
Now	O
lets	O
take	O
a	O
look	O
at	O
the	O
contents	O
of	O
a	O
PDDL1.2	O
domain	O
and	O
problem	O
description	O
in	O
general	O
...	O
The	O
domain	O
description	O
consisted	O
of	O
a	O
domain-name	O
definition	O
,	O
definition	O
of	O
requirements	O
(	O
to	O
declare	O
those	O
model-elements	O
to	O
the	O
planner	O
which	O
the	O
PDDL-model	O
is	O
actually	O
using	O
)	O
,	O
definition	O
of	O
object-type	O
hierarchy	O
(	O
just	O
like	O
a	O
class-hierarchy	O
in	O
OOP	B-Language
)	O
,	O
definition	O
of	O
constant	O
objects	O
(	O
which	O
are	O
present	O
in	O
every	O
problem	O
in	O
the	O
domain	O
)	O
,	O
definition	O
of	O
predicates	O
(	O
templates	O
for	O
logical	O
facts	O
)	O
,	O
and	O
also	O
the	O
definition	O
of	O
possible	O
actions	O
(	O
operator-schemas	O
with	O
parameters	O
,	O
which	O
should	O
be	O
grounded/instantiated	O
during	O
execution	O
)	O
.	O
</s>
<s>
to	O
maximize	O
the	O
number	O
of	O
satisfied	O
preferences	O
,	O
or	O
to	O
just	O
measure	O
the	O
quality	O
of	O
a	O
plan	O
)	O
to	O
enable	O
preference-based	B-Application
planning	I-Application
.	O
</s>
<s>
Thus	O
in	O
PDDL+	O
continuous	O
update	O
expressions	O
are	O
restricted	O
to	O
occur	O
only	O
in	O
process	O
effects	O
.	O
</s>
<s>
NDDL	O
(	O
New	O
Domain	O
Definition	O
Language	O
)	O
is	O
NASA	O
's	O
response	O
to	O
PDDL	B-Application
from	O
around	O
2002	O
.	O
</s>
<s>
Its	O
representation	O
differs	O
from	O
PDDL	B-Application
in	O
several	O
respects	O
:	O
1	O
)	O
it	O
uses	O
a	O
variable/value	O
representation	O
(	O
timelines/activities	O
)	O
rather	O
than	O
a	O
propositional/first	O
-order	O
logic	O
,	O
and	O
2	O
)	O
there	O
is	O
no	O
concept	O
of	O
states	O
or	O
actions	O
,	O
only	O
of	O
intervals	O
(	O
activities	O
)	O
and	O
constraints	O
between	O
those	O
activities	O
.	O
</s>
<s>
In	O
this	O
respect	O
,	O
models	O
in	O
NDDL	O
look	O
more	O
like	O
schemas	O
for	O
SAT	B-Algorithm
encodings	O
of	O
planning	O
problems	O
rather	O
than	O
PDDL	B-Application
models	O
.	O
</s>
<s>
during	O
critical	O
space	O
missions	O
)	O
may	O
be	O
more	O
robust	O
when	O
using	O
NDDL	O
,	O
but	O
the	O
correspondence	O
to	O
standard	O
planning-problem	O
representations	O
other	O
than	O
PDDL	B-Application
may	O
be	O
much	O
less	O
intuitive	O
than	O
in	O
case	O
of	O
PDDL	B-Application
.	O
</s>
<s>
Nonetheless	O
,	O
in	O
PDDL3.0	O
a	O
more	O
thorough	O
temporal	O
model	O
was	O
given	O
,	O
which	O
is	O
also	O
compatible	O
with	O
the	O
original	O
PDDL	B-Application
syntax	O
(	O
and	O
it	O
is	O
just	O
an	O
optional	O
addition	O
)	O
.	O
</s>
<s>
OPT	O
(	O
Ontology	O
with	O
Polymorphic	O
Types	O
)	O
was	O
a	O
profound	O
extension	O
of	O
PDDL2.1	O
by	O
Drew	O
McDermott	O
from	O
around	O
2003	O
–	O
2005	O
(	O
with	O
some	O
similarities	O
to	O
PDDL+	O
)	O
.	O
</s>
<s>
Its	O
syntax	O
was	O
based	O
on	O
PDDL	B-Application
,	O
but	O
it	O
had	O
a	O
much	O
more	O
elaborate	O
type	O
system	O
,	O
which	O
allowed	O
users	O
to	O
make	O
use	O
of	O
higher-order	O
constructs	O
such	O
as	O
explicit	O
λ-expressions	B-Language
allowing	O
for	O
efficient	O
type	O
inference	O
(	O
i.e.	O
</s>
<s>
The	O
notation	O
for	O
processes	O
and	O
durative	O
actions	O
was	O
borrowed	O
mainly	O
from	O
PDDL+	O
and	O
PDDL2.1	O
,	O
but	O
beyond	O
that	O
OPT	O
offered	O
many	O
other	O
significant	O
extensions	O
(	O
e.g.	O
</s>
<s>
data-structures	O
,	O
non-Boolean	O
fluents	O
,	O
return-values	O
for	O
actions	O
,	O
links	O
between	O
actions	O
,	O
hierarchical	O
action	O
expansion	O
,	O
hierarchy	O
of	O
domain	O
definitions	O
,	O
the	O
use	O
of	O
namespaces	B-Language
for	O
compatibility	O
with	O
the	O
semantic	O
web	O
)	O
.	O
</s>
<s>
PPDDL	B-Application
(	O
Probabilistic	O
PDDL	B-Application
)	O
1.0	O
was	O
the	O
official	O
language	O
of	O
the	O
probabilistic	O
track	O
of	O
the	O
and	O
IPC	O
in	O
2004	O
and	O
2006	O
respectively	O
.	O
</s>
<s>
APPL	O
(	O
Abstract	O
Plan	O
Preparation	O
Language	O
)	O
is	O
a	O
newer	O
variant	O
of	O
NDDL	O
from	O
2006	O
,	O
which	O
is	O
more	O
abstract	O
than	O
most	O
existing	O
planning	O
languages	O
such	O
as	O
PDDL	B-Application
or	O
NDDL	O
.	O
</s>
<s>
APPL	O
used	O
the	O
same	O
concepts	O
as	O
NDDL	O
with	O
the	O
extension	O
of	O
actions	O
,	O
and	O
also	O
some	O
other	O
concepts	O
,	O
but	O
still	O
its	O
expressive	O
power	O
is	O
much	O
less	O
than	O
PDDL	B-Application
's	O
(	O
in	O
hope	O
of	O
staying	O
robust	O
and	O
formally	O
verifiable	O
)	O
.	O
</s>
<s>
This	O
way	O
RDDL	O
departs	O
from	O
PDDL	B-Application
significantly	O
.	O
</s>
<s>
MA-PDDL	O
(	O
Multi	O
Agent	O
PDDL	B-Application
)	O
is	O
a	O
minimalistic	O
,	O
modular	O
extension	O
of	O
PDDL3.1	O
introduced	O
in	O
2012	O
(	O
i.e.	O
</s>
<s>
suppose	O
that	O
at	O
least	O
2	O
agents	O
are	O
needed	O
to	O
execute	O
a	O
lift	O
action	O
to	O
lift	O
a	O
heavy	O
table	O
into	O
the	O
air	O
,	O
or	O
otherwise	O
the	O
table	O
would	O
remain	O
on	O
the	O
ground	O
(	O
this	O
is	O
an	O
example	O
of	O
constructive	O
synergy	O
,	O
but	O
destructive	O
synergy	O
can	O
be	O
also	O
easily	O
represented	O
in	O
MA-PDDL	O
)	O
)	O
.	O
</s>
<s>
Moreover	O
,	O
as	O
kind	O
of	O
syntactic	O
sugar	O
,	O
a	O
simple	O
mechanism	O
for	O
the	O
inheritance	O
and	O
polymorphism	O
of	O
actions	O
,	O
goals	O
and	O
metrics	O
was	O
also	O
introduced	O
in	O
MA-PDDL	O
(	O
assuming	O
:typing	O
is	O
declared	O
)	O
.	O
</s>
<s>
Since	O
PDDL3.1	O
assumes	O
that	O
the	O
environment	O
is	O
deterministic	O
and	O
fully	O
observable	O
,	O
the	O
same	O
holds	O
for	O
MA-PDDL	O
,	O
i.e.	O
</s>
<s>
This	O
is	O
the	O
domain	O
definition	O
of	O
a	O
STRIPS	B-Application
instance	O
for	O
the	O
automated	B-Application
planning	I-Application
of	O
a	O
robot	O
with	O
two	O
gripper	O
arms	O
.	O
</s>
