<s>
Inductive	B-Application
logic	I-Application
programming	I-Application
(	O
ILP	O
)	O
is	O
a	O
subfield	O
of	O
symbolic	B-General_Concept
artificial	I-General_Concept
intelligence	I-General_Concept
which	O
uses	O
logic	B-Language
programming	I-Language
as	O
a	O
uniform	O
representation	O
for	O
examples	O
,	O
background	O
knowledge	O
and	O
hypotheses	O
.	O
</s>
<s>
Given	O
an	O
encoding	O
of	O
the	O
known	O
background	O
knowledge	O
and	O
a	O
set	O
of	O
examples	O
represented	O
as	O
a	O
logical	O
database	O
of	O
facts	O
,	O
an	O
ILP	O
system	O
will	O
derive	O
a	O
hypothesised	O
logic	B-Language
program	I-Language
which	O
entails	O
all	O
the	O
positive	O
and	O
none	O
of	O
the	O
negative	O
examples	O
.	O
</s>
<s>
Inductive	B-Application
logic	I-Application
programming	I-Application
is	O
particularly	O
useful	O
in	O
bioinformatics	O
and	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
<s>
Shapiro	O
built	O
their	O
first	O
implementation	O
(	O
Model	O
Inference	O
System	O
)	O
in	O
1981	O
:	O
a	O
Prolog	B-Language
program	O
that	O
inductively	O
inferred	O
logic	B-Language
programs	I-Language
from	O
positive	O
and	O
negative	O
examples	O
.	O
</s>
<s>
The	O
first	O
full	O
first-order	O
implementation	O
of	O
inductive	B-Application
logic	I-Application
programming	I-Application
was	O
Theorist	O
in	O
1986	O
.	O
</s>
<s>
The	O
term	O
Inductive	B-Application
Logic	I-Application
Programming	I-Application
was	O
first	O
introduced	O
in	O
a	O
paper	O
by	O
Stephen	O
Muggleton	O
in	O
1991	O
.	O
</s>
<s>
Muggleton	O
also	O
founded	O
the	O
annual	O
international	O
conference	O
on	O
Inductive	B-Application
Logic	I-Application
Programming	I-Application
,	O
introduced	O
the	O
theoretical	O
ideas	O
of	O
Predicate	O
Invention	O
,	O
Inverse	O
resolution	O
,	O
and	O
Inverse	O
entailment	O
.	O
</s>
<s>
Muggleton	O
implemented	O
Inverse	O
entailment	O
first	O
in	O
the	O
PROGOL	B-Application
system	O
.	O
</s>
<s>
suggesting	O
a	O
theory	O
to	O
explain	O
observed	O
facts	O
)	O
rather	O
than	O
mathematical	B-Algorithm
(	O
i.e.	O
</s>
<s>
proving	O
a	O
property	O
for	O
all	O
members	O
of	O
a	O
well-ordered	O
set	O
)	O
induction	B-Algorithm
.	O
</s>
<s>
The	O
background	O
knowledge	O
is	O
given	O
as	O
a	O
logic	O
theory	O
,	O
commonly	O
in	O
the	O
form	O
of	O
Horn	B-Application
clauses	I-Application
used	O
in	O
logic	B-Language
programming	I-Language
.	O
</s>
<s>
Plotkin	O
's	O
"	O
relative	O
least	O
general	O
generalization	O
(	O
rlgg	O
)	O
"	O
approach	O
to	O
inductive	B-Application
logic	I-Application
programming	I-Application
shall	O
be	O
used	O
to	O
obtain	O
a	O
suggestion	O
about	O
how	O
to	O
formally	O
define	O
the	O
daughter	O
relation	O
.	O
</s>
<s>
Convert	O
into	O
clause	B-Application
normal	I-Application
form	I-Application
:	O
</s>
<s>
Anti-unify	B-Application
each	O
compatible	O
pair	O
of	O
literals	O
:	O
</s>
<s>
The	O
resulting	O
Horn	B-Application
clause	I-Application
is	O
the	O
hypothesis	O
obtained	O
by	O
the	O
rlgg	O
approach	O
.	O
</s>
<s>
Historically	O
,	O
the	O
GOLEM	B-Application
implementation	O
is	O
based	O
on	O
the	O
rlgg	O
approach	O
.	O
</s>
<s>
Inductive	B-Application
Logic	I-Application
Programming	I-Application
system	O
is	O
a	O
program	O
that	O
takes	O
as	O
an	O
input	O
logic	O
theories	O
and	O
outputs	O
a	O
correct	O
hypothesis	O
wrt	O
theories	O
An	O
algorithm	O
of	O
an	O
ILP	O
system	O
consists	O
of	O
two	O
parts	O
:	O
hypothesis	O
search	O
and	O
hypothesis	O
selection	O
.	O
</s>
<s>
First	O
a	O
hypothesis	O
is	O
searched	O
with	O
an	O
inductive	B-Application
logic	I-Application
programming	I-Application
procedure	O
,	O
then	O
a	O
subset	O
of	O
the	O
found	O
hypotheses	O
(	O
in	O
most	O
systems	O
one	O
hypothesis	O
)	O
is	O
chosen	O
by	O
a	O
selection	O
algorithm	O
.	O
</s>
<s>
Modern	O
ILP	O
systems	O
like	O
Progol	B-Application
,	O
Hail	O
and	O
Imparo	O
find	O
a	O
hypothesis	O
using	O
the	O
principle	O
of	O
the	O
inverse	O
entailment	O
for	O
theories	O
,	O
,	O
:	O
.	O
</s>
<s>
For	O
example	O
,	O
Progol	B-Application
's	O
hypothesis	O
search	O
procedure	O
based	O
on	O
the	O
inverse	O
entailment	O
inference	O
rule	O
is	O
not	O
complete	O
by	O
Yamamoto	O
's	O
example	O
.	O
</s>
