<s>
OpenMath	B-Language
is	O
the	O
name	O
of	O
a	O
markup	O
language	O
for	O
specifying	O
the	O
meaning	O
of	O
mathematical	O
formulae	O
.	O
</s>
<s>
Among	O
other	O
things	O
,	O
it	O
can	O
be	O
used	O
to	O
complement	O
MathML	B-Language
,	O
a	O
standard	O
which	O
mainly	O
focuses	O
on	O
the	O
presentation	O
of	O
formulae	O
,	O
with	O
information	O
about	O
their	O
semantic	O
meaning	O
.	O
</s>
<s>
OpenMath	B-Language
can	O
be	O
encoded	O
in	O
XML	B-Protocol
or	O
in	O
a	O
binary	O
format	O
.	O
</s>
<s>
OpenMath	B-Language
consists	O
of	O
the	O
definition	O
of	O
"	O
OpenMath	B-Language
Objects	O
"	O
,	O
which	O
is	O
an	O
abstract	O
datatype	O
for	O
describing	O
the	O
logical	O
structure	O
of	O
a	O
mathematical	O
formula	O
and	O
the	O
definition	O
of	O
"	O
OpenMath	B-Language
Content	O
Dictionaries	O
"	O
,	O
or	O
collections	O
of	O
names	O
for	O
mathematical	O
concepts	O
.	O
</s>
<s>
The	O
names	O
available	O
from	O
the	O
latter	O
type	O
of	O
collections	O
are	O
specifically	O
intended	O
for	O
use	O
in	O
extending	O
MathML	B-Language
,	O
and	O
conversely	O
,	O
a	O
basic	O
set	O
of	O
such	O
"	O
Content	O
Dictionaries	O
"	O
has	O
been	O
designed	O
to	O
be	O
compatible	O
with	O
the	O
small	O
set	O
of	O
mathematical	O
concepts	O
defined	O
in	O
Content	O
MathML	B-Language
,	O
the	O
non-presentational	O
subset	O
of	O
MathML	B-Language
.	O
</s>
<s>
OpenMath	B-Language
has	O
been	O
developed	O
in	O
a	O
long	O
series	O
of	O
workshops	O
and	O
(	O
mostly	O
European	O
)	O
research	O
projects	O
that	O
began	O
in	O
1993	O
and	O
continues	O
through	O
today	O
.	O
</s>
<s>
The	O
OpenMath	B-Language
1.0	O
Standard	O
was	O
released	O
in	O
February	O
2000	O
,	O
and	O
revised	O
as	O
OpenMath	B-Language
1.1	O
in	O
October	O
2002	O
.	O
</s>
<s>
Two	O
years	O
later	O
,	O
the	O
OpenMath	B-Language
2.0	O
Standard	O
was	O
released	O
in	O
June	O
2004	O
.	O
</s>
<s>
OpenMath	B-Language
1	O
fixed	O
the	O
basic	O
language	O
architecture	O
,	O
while	O
OpenMath2	O
brought	O
better	O
XML	B-Protocol
integration	O
,	O
structure	O
sharing	O
and	O
liberalized	O
the	O
notion	O
of	O
OpenMath	B-Language
Content	O
dictionaries	O
.	O
</s>
<s>
The	O
OpenMath	B-Language
Effort	O
is	O
governed	O
by	O
the	O
OpenMath	B-Language
Society	O
,	O
based	O
in	O
Helsinki	O
,	O
Finland	O
.	O
</s>
<s>
Membership	O
is	O
by	O
invitation	O
of	O
the	O
Societies	O
Executive	O
Committee	O
,	O
which	O
welcomes	O
self-nominations	O
of	O
individuals	O
who	O
have	O
worked	O
on	O
OpenMath-related	O
issues	O
in	O
research	O
or	O
application	O
.	O
</s>
<s>
As	O
of	O
2007	O
,	O
Michael	O
Kohlhase	O
is	O
president	O
of	O
the	O
OpenMath	B-Language
society	O
.	O
</s>
<s>
would	O
be	O
marked	O
up	O
like	O
this	O
in	O
OpenMath	B-Language
(	O
the	O
representation	O
is	O
an	O
expression	O
tree	O
made	O
up	O
from	O
functional	O
elements	O
like	O
for	O
function	O
application	O
or	O
for	O
variables	O
)	O
:	O
</s>
<s>
Content	O
Dictionaries	O
are	O
structured	O
XML	B-Protocol
documents	I-Protocol
that	O
define	O
mathematical	O
symbols	O
that	O
can	O
be	O
referred	O
to	O
by	O
OMS	O
elements	O
in	O
OpenMath	B-Language
Objects	O
.	O
</s>
<s>
The	O
OpenMath	B-Language
2	O
standard	O
does	O
not	O
prescribe	O
a	O
canonical	O
encoding	O
for	O
content	O
dictionaries	O
,	O
but	O
only	O
requires	O
an	O
infrastructure	O
sufficient	O
for	O
unique	O
referencing	O
in	O
OMS	O
elements	O
.	O
</s>
<s>
OpenMath	B-Language
provides	O
a	O
very	O
basic	O
XML	B-Protocol
encoding	O
that	O
meets	O
these	O
requirements	O
,	O
and	O
a	O
set	O
of	O
specific	O
content	O
dictionaries	O
for	O
some	O
areas	O
of	O
mathematics	O
,	O
in	O
particular	O
covering	O
the	O
K-14	O
fragment	O
covered	O
by	O
content	O
MathML	B-Language
.	O
</s>
<s>
For	O
more	O
richly	O
structured	O
content	O
dictionaries	O
(	O
and	O
generally	O
for	O
arbitrary	O
mathematical	O
documents	O
)	O
the	O
OMDoc	B-Language
format	O
extends	O
OpenMath	B-Language
by	O
a	O
“	O
statement	O
level	O
”	O
(	O
including	O
structures	O
like	O
definitions	O
,	O
theorems	O
,	O
proofs	O
and	O
examples	O
,	O
as	O
well	O
as	O
means	O
for	O
interrelating	O
them	O
)	O
and	O
a	O
“	O
theory	O
level	O
”	O
,	O
where	O
a	O
theory	O
is	O
a	O
collection	O
of	O
several	O
contextually	O
related	O
statements	O
.	O
</s>
<s>
OMDoc	B-Language
's	O
theories	O
are	O
designed	O
to	O
be	O
compatible	O
to	O
OpenMath	B-Language
content	O
dictionaries	O
,	O
but	O
they	O
can	O
also	O
be	O
set	O
into	O
inheritance	O
and	O
import	O
relations	O
.	O
</s>
<s>
OpenMath	B-Language
is	O
criticised	O
for	O
being	O
inadequate	O
for	O
general	O
mathematics	O
,	O
exposing	O
not	O
enough	O
formal	O
precision	O
to	O
capture	O
the	O
intricacies	O
of	O
numerics	O
,	O
lacking	O
a	O
proof-of-concept	O
and	O
as	O
an	O
inferior	O
technology	O
to	O
already	O
established	O
approaches	O
of	O
encoding	O
mathematical	O
semantics	O
,	O
amongst	O
other	O
presumed	O
shortcomings	O
.	O
</s>
