<s>
Answer	B-Application
set	I-Application
programming	I-Application
(	O
ASP	O
)	O
is	O
a	O
form	O
of	O
declarative	B-Language
programming	I-Language
oriented	O
towards	O
difficult	O
(	O
primarily	O
NP-hard	O
)	O
search	B-Application
problems	I-Application
.	O
</s>
<s>
It	O
is	O
based	O
on	O
the	O
stable	B-Application
model	I-Application
(	O
answer	B-Application
set	I-Application
)	O
semantics	O
of	O
logic	B-Language
programming	I-Language
.	O
</s>
<s>
In	O
ASP	O
,	O
search	B-Application
problems	I-Application
are	O
reduced	O
to	O
computing	O
stable	B-Application
models	I-Application
,	O
and	O
answer	B-Application
set	I-Application
solvers	O
—	O
programs	O
for	O
generating	O
stable	B-Application
models	I-Application
—	O
are	O
used	O
to	O
perform	O
search	O
.	O
</s>
<s>
The	O
computational	O
process	O
employed	O
in	O
the	O
design	O
of	O
many	O
answer	B-Application
set	I-Application
solvers	O
is	O
an	O
enhancement	O
of	O
the	O
DPLL	B-Application
algorithm	I-Application
and	O
,	O
in	O
principle	O
,	O
it	O
always	O
terminates	O
(	O
unlike	O
Prolog	B-Language
query	O
evaluation	O
,	O
which	O
may	O
lead	O
to	O
an	O
infinite	B-Algorithm
loop	I-Algorithm
)	O
.	O
</s>
<s>
In	O
a	O
more	O
general	O
sense	O
,	O
ASP	O
includes	O
all	O
applications	O
of	O
answer	B-Application
sets	I-Application
to	O
knowledge	O
representation	O
and	O
the	O
use	O
of	O
Prolog-style	O
query	O
evaluation	O
for	O
solving	O
problems	O
arising	O
in	O
these	O
applications	O
.	O
</s>
<s>
An	O
early	O
example	O
of	O
answer	B-Application
set	I-Application
programming	I-Application
was	O
the	O
planning	B-Application
method	O
proposed	O
in	O
1997	O
by	O
Dimopoulos	O
,	O
Nebel	O
and	O
Köhler	O
.	O
</s>
<s>
Their	O
approach	O
is	O
based	O
on	O
the	O
relationship	O
between	O
plans	O
and	O
stable	B-Application
models	I-Application
.	O
</s>
<s>
applied	O
what	O
is	O
now	O
known	O
as	O
answer	B-Application
set	I-Application
programming	I-Application
to	O
the	O
problem	O
of	O
product	B-General_Concept
configuration	I-General_Concept
.	O
</s>
<s>
In	O
1999	O
,	O
the	O
term	O
"	O
answer	B-Application
set	I-Application
programming	I-Application
"	O
appeared	O
for	O
the	O
first	O
time	O
in	O
a	O
book	O
The	O
Logic	B-Language
Programming	I-Language
Paradigm	O
as	O
the	O
title	O
of	O
a	O
collection	O
of	O
two	O
papers	O
.	O
</s>
<s>
The	O
first	O
of	O
these	O
papers	O
identified	O
the	O
use	O
of	O
answer	B-Application
set	I-Application
solvers	O
for	O
search	O
as	O
a	O
new	O
programming	O
paradigm	O
.	O
</s>
<s>
That	O
same	O
year	O
Niemelä	O
also	O
proposed	O
"	O
logic	B-Language
programs	I-Language
with	O
stable	B-Application
model	I-Application
semantics	I-Application
"	O
as	O
a	O
new	O
paradigm	O
.	O
</s>
<s>
is	O
the	O
name	O
of	O
the	O
program	O
that	O
was	O
originally	O
created	O
as	O
a	O
grounding	O
tool	O
(	O
front-end	O
)	O
for	O
the	O
answer	B-Application
set	I-Application
solver	O
.	O
</s>
<s>
The	O
language	O
that	O
Lparse	O
accepts	O
is	O
now	O
commonly	O
called	O
AnsProlog	O
,	O
short	O
for	O
Answer	B-Application
Set	I-Application
Programming	I-Application
in	O
Logic	O
.	O
</s>
<s>
It	O
is	O
now	O
used	O
in	O
the	O
same	O
way	O
in	O
many	O
other	O
answer	B-Application
set	I-Application
solvers	O
,	O
including	O
,	O
,	O
,	O
,	O
and	O
.	O
</s>
<s>
(	O
is	O
an	O
exception	O
;	O
the	O
syntax	O
of	O
ASP	O
programs	O
written	O
for	O
dlv	B-Language
is	O
somewhat	O
different	O
.	O
)	O
</s>
<s>
says	O
:	O
choose	O
arbitrarily	O
which	O
of	O
the	O
atoms	O
to	O
include	O
in	O
the	O
stable	B-Application
model	I-Application
.	O
</s>
<s>
The	O
Lparse	O
program	O
that	O
contains	O
this	O
choice	O
rule	O
and	O
no	O
other	O
rules	O
has	O
8	O
stable	B-Application
models	I-Application
—	O
arbitrary	O
subsets	O
of	O
.	O
</s>
<s>
The	O
definition	O
of	O
a	O
stable	B-Application
model	I-Application
was	O
generalized	O
to	O
programs	O
with	O
choice	O
rules	O
.	O
</s>
<s>
Choice	O
rules	O
can	O
be	O
treated	O
also	O
as	O
abbreviations	O
for	O
propositional	O
formulas	O
under	O
the	O
stable	B-Application
model	I-Application
semantics	I-Application
.	O
</s>
<s>
Adding	O
this	O
constraint	O
to	O
an	O
Lparse	O
program	O
eliminates	O
the	O
stable	B-Application
models	I-Application
that	O
contain	O
at	O
least	O
2	O
of	O
the	O
atoms	O
.	O
</s>
<s>
Variables	O
(	O
capitalized	O
,	O
as	O
in	O
Prolog	B-Language
)	O
are	O
used	O
in	O
Lparse	O
to	O
abbreviate	O
collections	O
of	O
rules	O
that	O
follow	O
the	O
same	O
pattern	O
,	O
and	O
also	O
to	O
abbreviate	O
collections	O
of	O
atoms	O
within	O
the	O
same	O
rule	O
.	O
</s>
<s>
Option	O
0	O
instructs	O
smodels	O
to	O
find	O
all	O
stable	B-Application
models	I-Application
of	O
the	O
program	O
.	O
</s>
<s>
However	O
,	O
the	O
search	O
process	O
employed	O
by	O
smodels	O
and	O
other	O
answer	B-Application
set	I-Application
solvers	O
is	O
not	O
based	O
on	O
trial	O
and	O
error	O
.	O
</s>
<s>
In	O
natural	B-Language
language	I-Language
processing	I-Language
,	O
dependency-based	B-Language
parsing	I-Language
can	O
be	O
formulated	O
as	O
an	O
ASP	O
problem	O
.	O
</s>
<s>
The	O
following	O
code	O
parses	B-Language
the	O
Latin	O
sentence	O
"	O
Puella	O
pulchra	O
in	O
villa	O
linguam	O
latinam	O
discit	O
"	O
,	O
"	O
the	O
pretty	O
girl	O
is	O
learning	O
Latin	O
in	O
the	O
villa	O
"	O
.	O
</s>
<s>
ASP-Core-2	O
is	O
the	O
reference	O
language	O
for	O
the	O
Answer	B-Application
Set	I-Application
Programming	I-Application
Competition	O
,	O
in	O
which	O
ASP	O
solvers	O
are	O
periodically	O
benchmarked	O
over	O
a	O
number	O
of	O
reference	O
problems	O
.	O
</s>
<s>
Early	O
systems	O
,	O
such	O
as	O
Smodels	O
,	O
used	O
backtracking	B-Algorithm
to	O
find	O
solutions	O
.	O
</s>
<s>
These	O
approaches	O
allow	O
for	O
significant	O
improvements	O
of	O
performance	O
,	O
often	O
by	O
an	O
order	O
of	O
magnitude	O
,	O
over	O
earlier	O
backtracking	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
The	O
project	O
acts	O
as	O
an	O
umbrella	O
for	O
many	O
of	O
the	O
systems	O
below	O
,	O
including	O
clasp	O
,	O
grounding	O
systems	O
(	O
gringo	O
)	O
,	O
incremental	O
systems	O
(	O
iclingo	O
)	O
,	O
constraint	O
solvers	O
(	O
clingcon	O
)	O
,	O
action	B-Application
language	I-Application
to	O
ASP	O
compilers	O
(	O
coala	O
)	O
,	O
distributed	O
MPI	O
implementations	O
(	O
claspar	O
)	O
,	O
and	O
many	O
others	O
.	O
</s>
<s>
Query-driven	O
implementations	O
of	O
answer	B-Application
set	I-Application
programming	I-Application
,	O
such	O
as	O
the	O
Galliwasp	O
system	O
and	O
s(CASP )	O
avoid	O
grounding	O
altogether	O
by	O
using	O
a	O
combination	O
of	O
resolution	O
and	O
coinduction	B-Application
.	O
</s>
<s>
Platform	O
Features	O
Mechanics	O
Name	O
OS	O
Licence	O
Variables	O
Function	O
symbols	O
Explicit	O
sets	O
Explicit	O
lists	O
Disjunctive	O
(	O
choice	O
rules	O
)	O
supportASPeRiXLinuxGPLon-the-fly	O
groundingASSATSolarisFreewareSAT-solver	O
basedClasp	O
Answer	B-Application
Set	I-Application
SolverLinux	O
,	O
macOS	B-Application
,	O
WindowsMIT	O
Licenseincremental	O
,	O
SAT-solver	O
inspired	O
(	O
nogood	O
,	O
conflict-driven	O
)	O
CmodelsLinux	O
,	O
SolarisGPLincremental	O
,	O
SAT-solver	O
inspired	O
(	O
nogood	O
,	O
conflict-driven	O
)	O
diff-SATLinux	O
,	O
macOS	B-Application
,	O
Windows	B-Application
(	O
Java	B-Language
virtual	I-Language
machine	I-Language
)	O
MIT	O
LicenseSAT-solver	O
inspired	O
(	O
nogood	O
,	O
conflict-driven	O
)	O
.	O
</s>
