<s>
Description	B-Language
logics	I-Language
(	O
DL	O
)	O
are	O
a	O
family	O
of	O
formal	O
knowledge	O
representation	O
languages	O
.	O
</s>
<s>
There	O
are	O
general	O
,	O
spatial	O
,	O
temporal	O
,	O
spatiotemporal	O
,	O
and	O
fuzzy	O
description	B-Language
logics	I-Language
,	O
and	O
each	O
description	B-Language
logic	I-Language
features	O
a	O
different	O
balance	O
between	O
expressive	B-Language
power	I-Language
and	O
reasoning	O
complexity	O
by	O
supporting	O
different	O
sets	O
of	O
mathematical	O
constructors	O
.	O
</s>
<s>
DLs	O
are	O
used	O
in	O
artificial	B-Application
intelligence	I-Application
to	O
describe	O
and	O
reason	O
about	O
the	O
relevant	O
concepts	O
of	O
an	O
application	O
domain	O
(	O
known	O
as	O
terminological	O
knowledge	O
)	O
.	O
</s>
<s>
It	O
is	O
of	O
particular	O
importance	O
in	O
providing	O
a	O
logical	O
formalism	O
for	O
ontologies	B-Language
and	O
the	O
Semantic	O
Web	O
:	O
the	O
Web	B-Language
Ontology	I-Language
Language	I-Language
(	O
OWL	B-Language
)	O
and	O
its	O
profiles	O
are	O
based	O
on	O
DLs	O
.	O
</s>
<s>
The	O
most	O
notable	O
application	O
of	O
DLs	O
and	O
OWL	B-Language
is	O
in	O
biomedical	O
informatics	O
where	O
DL	O
assists	O
in	O
the	O
codification	O
of	O
biomedical	O
knowledge	O
.	O
</s>
<s>
A	O
description	B-Language
logic	I-Language
(	O
DL	O
)	O
models	O
concepts	O
,	O
roles	O
and	O
individuals	O
,	O
and	O
their	O
relationships	O
.	O
</s>
<s>
The	O
fundamental	O
modeling	O
concept	O
of	O
a	O
DL	O
is	O
the	O
axiom	B-Algorithm
—	O
a	O
logical	O
statement	O
relating	O
roles	O
and/or	O
concepts	O
.	O
</s>
<s>
The	O
description	B-Language
logic	I-Language
community	O
uses	O
different	O
terminology	O
than	O
the	O
first-order	O
logic	O
(	O
FOL	O
)	O
community	O
for	O
operationally	O
equivalent	O
notions	O
;	O
some	O
examples	O
are	O
given	O
below	O
.	O
</s>
<s>
The	O
Web	B-Language
Ontology	I-Language
Language	I-Language
(	O
OWL	B-Language
)	O
uses	O
again	O
a	O
different	O
terminology	O
,	O
also	O
given	O
in	O
the	O
table	O
below	O
.	O
</s>
<s>
There	O
are	O
many	O
varieties	O
of	O
description	B-Language
logics	I-Language
and	O
there	O
is	O
an	O
informal	O
naming	O
convention	O
,	O
roughly	O
describing	O
the	O
operators	O
allowed	O
.	O
</s>
<s>
The	O
expressivity	B-Language
is	O
encoded	O
in	O
the	O
label	O
for	O
a	O
logic	O
starting	O
with	O
one	O
of	O
the	O
following	O
basic	O
logics	O
:	O
</s>
<s>
Limited	O
complex	O
role	O
inclusion	O
axioms	B-Algorithm
;	O
reflexivity	O
and	O
irreflexivity	O
;	O
role	O
disjointness	O
.	O
</s>
<s>
(	O
Enumerated	O
classes	O
of	O
object	O
value	O
restrictions	O
:	O
owl:oneOf	O
,	O
owl:hasValue	O
)	O
.	O
</s>
<s>
Cardinality	O
restrictions	O
(	O
owl:cardinality	O
,	O
owl:maxCardinality	O
)	O
,	O
a	O
special	O
case	O
of	O
counting	B-Algorithm
quantification	I-Algorithm
Qualified	O
cardinality	O
restrictions	O
(	O
available	O
in	O
OWL	B-Language
2	I-Language
,	O
cardinality	O
restrictions	O
that	O
have	O
fillers	O
other	O
than	O
)	O
.	O
</s>
<s>
A	O
sub-language	O
of	O
,	O
which	O
is	O
obtained	O
by	O
disallowing	O
limited	O
existential	B-Algorithm
quantification	I-Algorithm
.	O
</s>
<s>
As	O
an	O
example	O
,	O
is	O
a	O
centrally	O
important	O
description	B-Language
logic	I-Language
from	O
which	O
comparisons	O
with	O
other	O
varieties	O
can	O
be	O
made	O
.	O
</s>
<s>
A	O
further	O
example	O
,	O
the	O
description	B-Language
logic	I-Language
is	O
the	O
logic	O
plus	O
extended	O
cardinality	O
restrictions	O
,	O
and	O
transitive	O
and	O
inverse	O
roles	O
.	O
</s>
<s>
The	O
Protégé	B-Language
ontology	B-Language
editor	O
supports	O
.	O
</s>
<s>
OWL	B-Language
2	I-Language
provides	O
the	O
expressiveness	O
of	O
,	O
OWL-DL	O
is	O
based	O
on	O
,	O
and	O
for	O
OWL-Lite	O
it	O
is	O
.	O
</s>
<s>
Description	B-Language
logic	I-Language
was	O
given	O
its	O
current	O
name	O
in	O
the	O
1980s	O
.	O
</s>
<s>
Frames	O
and	O
semantic	O
networks	O
lack	O
formal	O
(	O
logic-based	O
)	O
semantics	B-Application
.	O
</s>
<s>
The	O
first	O
DL-based	O
KR	O
system	O
was	O
KL-ONE	B-Language
(	O
by	O
Ronald	O
J	O
.	O
Brachman	O
and	O
Schmolze	O
,	O
1985	O
)	O
.	O
</s>
<s>
During	O
the	O
'	O
80s	O
other	O
DL-based	O
systems	O
using	O
structural	O
subsumption	O
algorithms	O
were	O
developed	O
including	O
KRYPTON	B-Language
(	O
1983	O
)	O
,	O
LOOM	B-Language
(	O
1987	O
)	O
,	O
BACK	O
(	O
1988	O
)	O
,	O
K-REP	O
(	O
1991	O
)	O
and	O
CLASSIC	O
(	O
1991	O
)	O
.	O
</s>
<s>
Examples	O
from	O
this	O
period	O
include	O
FaCT	O
,	O
RACER	O
(	O
2001	O
)	O
,	O
CEL	O
(	O
2005	O
)	O
,	O
and	O
KAON	B-Application
2	I-Application
(	O
2005	O
)	O
.	O
</s>
<s>
DL	O
reasoners	O
,	O
such	O
as	O
FaCT	O
,	O
FaCT++	B-Language
,	O
RACER	O
,	O
DLP	O
and	O
Pellet	B-Language
,	O
implement	O
the	O
method	O
of	O
analytic	O
tableaux	O
.	O
</s>
<s>
KAON2	B-Application
is	O
implemented	O
by	O
algorithms	O
which	O
reduce	O
a	O
SHIQ(D )	O
knowledge	O
base	O
to	O
a	O
disjunctive	O
datalog	B-Language
program	O
.	O
</s>
<s>
In	O
particular	O
,	O
the	O
formal	O
semantics	B-Application
and	O
reasoning	O
in	O
OIL	O
use	O
the	O
DL	O
.	O
</s>
<s>
The	O
DAML+OIL	O
DL	O
was	O
developed	O
as	O
a	O
submission	O
to	O
—	O
and	O
formed	O
the	O
starting	O
point	O
of	O
—	O
the	O
World	O
Wide	O
Web	O
Consortium	O
(	O
W3C	O
)	O
Web	O
Ontology	B-Language
Working	O
Group	O
.	O
</s>
<s>
In	O
2004	O
,	O
the	O
Web	O
Ontology	B-Language
Working	O
Group	O
completed	O
its	O
work	O
by	O
issuing	O
the	O
OWL	B-Language
recommendation	O
.	O
</s>
<s>
The	O
design	O
of	O
OWL	B-Language
is	O
based	O
on	O
the	O
family	O
of	O
DL	O
with	O
OWL	B-Language
DL	O
and	O
OWL	B-Language
Lite	O
based	O
on	O
and	O
respectively	O
.	O
</s>
<s>
The	O
W3C	O
OWL	B-Language
Working	O
Group	O
began	O
work	O
in	O
2007	O
on	O
a	O
refinement	O
of	O
-	O
and	O
extension	O
to	O
-	O
OWL	B-Language
.	O
</s>
<s>
In	O
2009	O
,	O
this	O
was	O
completed	O
by	O
the	O
issuance	O
of	O
the	O
OWL2	B-Language
recommendation	O
.	O
</s>
<s>
OWL2	B-Language
is	O
based	O
on	O
the	O
description	B-Language
logic	I-Language
.	O
</s>
<s>
Practical	O
experience	O
demonstrated	O
that	O
OWL	B-Language
DL	O
lacked	O
several	O
key	O
features	O
necessary	O
to	O
model	O
complex	O
domains	O
.	O
</s>
<s>
In	O
DL	O
,	O
a	O
distinction	O
is	O
drawn	O
between	O
the	O
so-called	O
TBox	B-General_Concept
(	O
terminological	O
box	O
)	O
and	O
the	O
ABox	B-General_Concept
(	O
assertional	O
box	O
)	O
.	O
</s>
<s>
In	O
general	O
,	O
the	O
TBox	B-General_Concept
contains	O
sentences	O
describing	O
concept	O
hierarchies	O
(	O
i.e.	O
,	O
relations	O
between	O
concepts	O
)	O
while	O
the	O
ABox	B-General_Concept
contains	O
ground	O
sentences	O
stating	O
where	O
in	O
the	O
hierarchy	O
,	O
individuals	O
belong	O
(	O
i.e.	O
,	O
relations	O
between	O
individuals	O
and	O
concepts	O
)	O
.	O
</s>
<s>
belongs	O
in	O
the	O
TBox	B-General_Concept
,	O
while	O
the	O
statement	O
:	O
</s>
<s>
belongs	O
in	O
the	O
ABox	B-General_Concept
.	O
</s>
<s>
Note	O
that	O
the	O
TBox/ABox	O
distinction	O
is	O
not	O
significant	O
,	O
in	O
the	O
same	O
sense	O
that	O
the	O
two	O
"	O
kinds	O
"	O
of	O
sentences	O
are	O
not	O
treated	O
differently	O
in	O
first-order	O
logic	O
(	O
which	O
subsumes	O
most	O
DL	O
)	O
.	O
</s>
<s>
When	O
translated	O
into	O
first-order	O
logic	O
,	O
a	O
subsumption	O
axiom	B-Algorithm
like	O
(	O
)	O
is	O
simply	O
a	O
conditional	O
restriction	O
to	O
unary	O
predicates	B-Algorithm
(	O
concepts	O
)	O
with	O
only	O
variables	O
appearing	O
in	O
it	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
reasoner	O
might	O
process	O
the	O
TBox	B-General_Concept
and	O
ABox	B-General_Concept
separately	O
,	O
in	O
part	O
because	O
certain	O
key	O
inference	O
problems	O
are	O
tied	O
to	O
one	O
but	O
not	O
the	O
other	O
one	O
( 	O
 '	O
classification	O
 '	O
is	O
related	O
to	O
the	O
TBox	B-General_Concept
,	O
'	O
instance	O
checking	O
 '	O
to	O
the	O
ABox	B-General_Concept
)	O
.	O
</s>
<s>
Another	O
example	O
is	O
that	O
the	O
complexity	O
of	O
the	O
TBox	B-General_Concept
can	O
greatly	O
affect	O
the	O
performance	O
of	O
a	O
given	O
decision-procedure	O
for	O
a	O
certain	O
DL	O
,	O
independently	O
of	O
the	O
ABox	B-General_Concept
.	O
</s>
<s>
It	O
is	O
plausible	O
to	O
distinguish	O
between	O
our	O
conception	O
of	O
terms/concepts	O
in	O
the	O
world	O
(	O
class	O
axioms	B-Algorithm
in	O
the	O
TBox	B-General_Concept
)	O
and	O
particular	O
manifestations	O
of	O
those	O
terms/concepts	O
(	O
instance	O
assertions	O
in	O
the	O
ABox	B-General_Concept
)	O
.	O
</s>
<s>
In	O
the	O
above	O
example	O
:	O
when	O
the	O
hierarchy	O
within	O
a	O
company	O
is	O
the	O
same	O
in	O
every	O
branch	O
but	O
the	O
assignment	O
to	O
employees	O
is	O
different	O
in	O
every	O
department	O
(	O
because	O
there	O
are	O
other	O
people	O
working	O
there	O
)	O
,	O
it	O
makes	O
sense	O
to	O
reuse	O
the	O
TBox	B-General_Concept
for	O
different	O
branches	O
that	O
do	O
not	O
use	O
the	O
same	O
ABox	B-General_Concept
.	O
</s>
<s>
There	O
are	O
two	O
features	O
of	O
description	B-Language
logic	I-Language
that	O
are	O
not	O
shared	O
by	O
most	O
other	O
data	O
description	O
formalisms	O
:	O
DL	O
does	O
not	O
make	O
the	O
unique	O
name	O
assumption	O
(	O
UNA	O
)	O
or	O
the	O
closed-world	B-Application
assumption	I-Application
(	O
CWA	O
)	O
.	O
</s>
<s>
Not	O
having	O
CWA	O
,	O
or	O
rather	O
having	O
the	O
open	B-Application
world	I-Application
assumption	I-Application
(	O
OWA	O
)	O
means	O
that	O
lack	O
of	O
knowledge	O
of	O
a	O
fact	O
does	O
not	O
immediately	O
imply	O
knowledge	O
of	O
the	O
negation	O
of	O
a	O
fact	O
.	O
</s>
<s>
Like	O
first-order	O
logic	O
(	O
FOL	O
)	O
,	O
a	O
syntax	O
defines	O
which	O
collections	O
of	O
symbols	O
are	O
legal	O
expressions	O
in	O
a	O
description	B-Language
logic	I-Language
,	O
and	O
semantics	B-Application
determine	O
meaning	O
.	O
</s>
<s>
The	O
syntax	O
of	O
a	O
member	O
of	O
the	O
description	B-Language
logic	I-Language
family	O
is	O
characterized	O
by	O
its	O
recursive	O
definition	O
,	O
in	O
which	O
the	O
constructors	O
that	O
can	O
be	O
used	O
to	O
form	O
concept	O
terms	O
are	O
stated	O
.	O
</s>
<s>
Some	O
constructors	O
are	O
related	O
to	O
logical	O
constructors	O
in	O
first-order	O
logic	O
(	O
FOL	O
)	O
such	O
as	O
intersection	O
or	O
conjunction	O
of	O
concepts	O
,	O
union	O
or	O
disjunction	O
of	O
concepts	O
,	O
negation	O
or	O
complement	O
of	O
concepts	O
,	O
universal	O
restriction	O
and	O
existential	B-Algorithm
restriction	I-Algorithm
.	O
</s>
<s>
If	O
a	B-Application
is	I-Application
R-related	O
to	O
b	O
,	O
then	O
b	O
is	O
called	O
an	O
R-successor	O
of	O
a	O
.	O
</s>
<s>
A	O
TBox	B-General_Concept
is	O
any	O
finite	O
set	O
of	O
GCIs	O
.	O
</s>
<s>
An	O
ABox	B-General_Concept
is	O
a	O
finite	O
set	O
of	O
assertional	O
axioms	B-Algorithm
.	O
</s>
<s>
A	O
knowledge	O
base	O
(	O
KB	O
)	O
is	O
an	O
ordered	O
pair	O
for	O
TBox	B-General_Concept
and	O
ABox	B-General_Concept
.	O
</s>
<s>
The	O
semantics	B-Application
of	O
description	B-Language
logics	I-Language
are	O
defined	O
by	O
interpreting	O
concepts	O
as	O
sets	O
of	O
individuals	O
and	O
roles	O
as	O
sets	O
of	O
ordered	O
pairs	O
of	O
individuals	O
.	O
</s>
<s>
The	O
semantics	B-Application
of	O
non-atomic	O
concepts	O
and	O
roles	O
is	O
then	O
defined	O
in	O
terms	O
of	O
atomic	O
concepts	O
and	O
roles	O
.	O
</s>
<s>
The	O
most	O
common	O
decision	O
problems	O
are	O
basic	O
database-query-like	O
questions	O
like	O
instance	O
checking	O
(	O
is	O
a	O
particular	O
instance	O
(	O
member	O
of	O
an	O
ABox	B-General_Concept
)	O
a	O
member	O
of	O
a	O
given	O
concept	O
)	O
and	O
relation	O
checking	O
(	O
does	O
a	O
relation/role	O
hold	O
between	O
two	O
instances	O
,	O
in	O
other	O
words	O
does	O
a	O
have	O
property	O
b	O
)	O
,	O
and	O
the	O
more	O
global-database-questions	O
like	O
subsumption	O
(	O
is	O
a	O
concept	O
a	O
subset	O
of	O
another	O
concept	O
)	O
,	O
and	O
concept	O
consistency	O
(	O
is	O
there	O
no	O
contradiction	O
among	O
the	O
definitions	O
or	O
chain	O
of	O
definitions	O
)	O
.	O
</s>
<s>
The	O
more	O
operators	O
one	O
includes	O
in	O
a	O
logic	O
and	O
the	O
more	O
complicated	O
the	O
TBox	B-General_Concept
(	O
having	O
cycles	O
,	O
allowing	O
non-atomic	O
concepts	O
to	O
include	O
each	O
other	O
)	O
,	O
usually	O
the	O
higher	O
the	O
computational	O
complexity	O
is	O
for	O
each	O
of	O
these	O
problems	O
(	O
see	O
for	O
examples	O
)	O
.	O
</s>
<s>
Fuzzy	O
description	B-Language
logics	I-Language
combines	O
fuzzy	O
logic	O
with	O
DLs	O
.	O
</s>
<s>
Since	O
many	O
concepts	O
that	O
are	O
needed	O
for	O
intelligent	B-Application
systems	I-Application
lack	O
well	O
defined	O
boundaries	O
,	O
or	O
precisely	O
defined	O
criteria	O
of	O
membership	O
,	O
fuzzy	O
logic	O
is	O
needed	O
to	O
deal	O
with	O
notions	O
of	O
vagueness	O
and	O
imprecision	O
.	O
</s>
<s>
This	O
offers	O
a	O
motivation	O
for	O
a	O
generalization	O
of	O
description	B-Language
logic	I-Language
towards	O
dealing	O
with	O
imprecise	O
and	O
vague	O
concepts	O
.	O
</s>
<s>
Description	B-Language
logic	I-Language
is	O
related	O
to	O
—	O
but	O
developed	O
independently	O
of	O
—	O
modal	O
logic	O
(	O
ML	O
)	O
.	O
</s>
<s>
Temporal	O
description	B-Language
logic	I-Language
represents	O
—	O
and	O
allows	O
reasoning	O
about	O
—	O
time	O
dependent	O
concepts	O
and	O
many	O
different	O
approaches	O
to	O
this	O
problem	O
exist	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
description	B-Language
logic	I-Language
might	O
be	O
combined	O
with	O
a	O
modal	O
temporal	O
logic	O
such	O
as	O
linear	O
temporal	O
logic	O
.	O
</s>
