<s>
Abductive	B-Application
logic	I-Application
programming	I-Application
(	O
ALP	O
)	O
is	O
a	O
high-level	O
knowledge-representation	O
framework	O
that	O
can	O
be	O
used	O
to	O
solve	O
problems	O
declaratively	O
based	O
on	O
abductive	O
reasoning	O
.	O
</s>
<s>
It	O
extends	O
normal	O
logic	B-Language
programming	I-Language
by	O
allowing	O
some	O
predicates	O
to	O
be	O
incompletely	O
defined	O
,	O
declared	O
as	O
abducible	O
predicates	O
.	O
</s>
<s>
These	O
problems	O
can	O
be	O
either	O
observations	O
that	O
need	O
to	O
be	O
explained	O
(	O
as	O
in	O
classical	O
abduction	O
)	O
or	O
goals	O
to	O
be	O
achieved	O
(	O
as	O
in	O
normal	O
logic	B-Language
programming	I-Language
)	O
.	O
</s>
<s>
It	O
has	O
also	O
been	O
used	O
to	O
interpret	O
negation	B-Application
as	I-Application
failure	I-Application
as	O
a	O
form	O
of	O
abductive	O
reasoning	O
.	O
</s>
<s>
Abductive	O
logic	B-Language
programs	I-Language
have	O
three	O
components	O
,	O
where	O
:	O
</s>
<s>
Normally	O
,	O
the	O
logic	B-Language
program	I-Language
P	O
does	O
not	O
contain	O
any	O
clauses	O
whose	O
head	O
(	O
or	O
conclusion	O
)	O
refers	O
to	O
an	O
abducible	O
predicate	O
.	O
</s>
<s>
An	O
abductive	O
explanation	O
of	O
a	O
problem	O
G	O
is	O
a	O
set	O
of	O
positive	O
(	O
and	O
sometimes	O
also	O
negative	O
)	O
ground	O
instances	O
of	O
the	O
abducible	O
predicates	O
,	O
such	O
that	O
,	O
when	O
these	O
are	O
added	O
to	O
the	O
logic	B-Language
program	I-Language
P	O
,	O
the	O
problem	O
G	O
and	O
the	O
integrity	O
constraints	O
IC	O
both	O
hold	O
.	O
</s>
<s>
Thus	O
abductive	O
explanations	O
extend	O
the	O
logic	B-Language
program	I-Language
P	O
by	O
the	O
addition	O
of	O
full	O
or	O
partial	O
definitions	O
of	O
the	O
abducible	O
predicates	O
.	O
</s>
<s>
Computation	O
in	O
ALP	O
combines	O
the	O
backwards	O
reasoning	O
of	O
normal	O
logic	B-Language
programming	I-Language
(	O
to	O
reduce	O
problems	O
to	O
sub-problems	O
)	O
with	O
a	O
kind	O
of	O
integrity	O
checking	O
to	O
show	O
that	O
the	O
abductive	O
explanations	O
satisfy	O
the	O
integrity	O
constraints	O
.	O
</s>
<s>
The	O
abductive	O
logic	B-Language
program	I-Language
,	O
,	O
has	O
in	O
the	O
following	O
sentences	O
:	O
</s>
<s>
Consider	O
the	O
abductive	O
logic	B-Language
program	I-Language
consisting	O
of	O
the	O
following	O
(	O
simplified	O
)	O
clauses	O
:	O
</s>
<s>
The	O
abductive	O
logic	B-Language
program	I-Language
below	O
describes	O
a	O
simple	O
model	O
of	O
the	O
lactose	O
metabolism	O
of	O
the	O
bacterium	O
E	O
.	O
coli	O
.	O
</s>
<s>
Given	O
an	O
abductive	O
logic	B-Language
program	I-Language
,	O
,	O
an	O
abductive	O
explanation	O
for	O
a	O
problem	O
is	O
a	O
set	O
of	O
ground	O
atoms	O
on	O
abducible	O
predicates	O
such	O
that	O
:	O
</s>
<s>
This	O
definition	O
leaves	O
open	O
the	O
choice	O
of	O
the	O
underlying	O
semantics	O
of	O
logic	B-Language
programming	I-Language
through	O
which	O
we	O
give	O
the	O
exact	O
meaning	O
of	O
the	O
entailment	O
relation	O
and	O
the	O
notion	O
of	O
consistency	O
of	O
the	O
(	O
extended	O
)	O
logic	B-Language
programs	I-Language
.	O
</s>
<s>
Any	O
of	O
the	O
different	O
semantics	O
of	O
logic	B-Language
programming	I-Language
such	O
as	O
the	O
completion	O
,	O
stable	O
or	O
well-founded	O
semantics	O
can	O
(	O
and	O
have	O
been	O
used	O
in	O
practice	O
)	O
to	O
give	O
different	O
notions	O
of	O
abductive	O
explanations	O
and	O
thus	O
different	O
forms	O
of	O
ALP	O
frameworks	O
.	O
</s>
<s>
It	O
requires	O
that	O
these	O
are	O
entailed	O
by	O
the	O
logic	B-Language
program	I-Language
extended	O
with	O
an	O
abductive	O
solution	O
,	O
thus	O
meaning	O
that	O
in	O
any	O
model	O
of	O
the	O
extended	O
logic	B-Language
program	I-Language
(	O
which	O
one	O
can	O
think	O
of	O
as	O
an	O
ensuing	O
world	O
given	O
)	O
the	O
requirements	O
of	O
the	O
integrity	O
constraints	O
are	O
met	O
.	O
</s>
<s>
In	O
practice	O
,	O
in	O
many	O
cases	O
these	O
two	O
ways	O
of	O
formalizing	O
the	O
role	O
of	O
the	O
integrity	O
constraints	O
coincide	O
as	O
the	O
logic	B-Language
program	I-Language
and	O
its	O
extensions	O
always	O
have	O
a	O
unique	O
model	O
.	O
</s>
<s>
Most	O
of	O
the	O
implementations	O
of	O
ALP	O
extend	O
the	O
SLD	O
resolution-based	O
computational	O
model	O
of	O
logic	B-Language
programming	I-Language
.	O
</s>
<s>
ALP	O
can	O
also	O
be	O
implemented	O
by	O
means	O
of	O
its	O
link	O
with	O
Answer	B-Application
Set	I-Application
Programming	I-Application
(	O
ASP	O
)	O
,	O
where	O
the	O
ASP	O
systems	O
can	O
be	O
employed	O
.	O
</s>
