<s>
DisCoCat	B-General_Concept
(	O
Categorical	O
Compositional	O
Distributional	O
)	O
is	O
a	O
mathematical	O
framework	O
for	O
natural	B-Language
language	I-Language
processing	I-Language
which	O
uses	O
category	O
theory	O
to	O
unify	O
distributional	O
semantics	B-Application
with	O
the	O
principle	O
of	O
compositionality	O
.	O
</s>
<s>
The	O
grammatical	O
derivations	O
in	O
a	O
categorial	O
grammar	O
(	O
usually	O
a	O
pregroup	O
grammar	O
)	O
are	O
interpreted	O
as	O
linear	B-Architecture
maps	I-Architecture
acting	O
on	O
the	O
tensor	O
product	O
of	O
word	B-General_Concept
vectors	I-General_Concept
to	O
produce	O
the	O
meaning	O
of	O
a	O
sentence	O
or	O
a	O
piece	O
of	O
text	O
.	O
</s>
<s>
String	O
diagrams	O
are	O
used	O
to	O
visualise	O
information	O
flow	O
and	O
reason	O
about	O
natural	O
language	O
semantics	B-Application
.	O
</s>
<s>
The	O
framework	O
was	O
first	O
introduced	O
by	O
Bob	O
Coecke	O
,	O
Mehrnoosh	O
Sadrzadeh	O
,	O
and	O
Stephen	O
Clark	O
as	O
an	O
application	O
of	O
categorical	O
quantum	O
mechanics	O
to	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
<s>
Although	O
the	O
analogy	O
with	O
quantum	O
mechanics	O
was	O
kept	O
informal	O
at	O
first	O
,	O
it	O
eventually	O
led	O
to	O
the	O
development	O
of	O
quantum	B-Device
natural	I-Device
language	I-Device
processing	I-Device
.	O
</s>
<s>
There	O
are	O
multiple	O
definitions	O
of	O
DisCoCat	B-General_Concept
in	O
the	O
literature	O
,	O
depending	O
on	O
the	O
choice	O
made	O
for	O
the	O
compositional	O
aspect	O
of	O
the	O
model	O
.	O
</s>
<s>
The	O
common	O
denominator	O
between	O
all	O
the	O
existent	O
versions	O
,	O
however	O
,	O
always	O
involves	O
a	O
categorical	O
definition	O
of	O
DisCoCat	B-General_Concept
as	O
a	O
structure-preserving	O
functor	O
from	O
a	O
category	O
of	O
grammar	O
to	O
a	O
category	O
of	O
semantics	B-Application
,	O
which	O
usually	O
encodes	O
the	O
distributional	O
hypothesis	O
.	O
</s>
<s>
With	O
this	O
definition	O
of	O
pregroup	O
grammars	O
as	O
free	O
rigid	O
categories	O
,	O
DisCoCat	B-General_Concept
models	O
can	O
be	O
defined	O
as	O
strong	O
monoidal	O
functors	O
.	O
</s>
<s>
The	O
meaning	O
of	O
a	O
sentence	O
is	O
then	O
given	O
by	O
a	O
vector	O
which	O
can	O
be	O
computed	O
as	O
the	O
contraction	O
of	O
a	O
tensor	B-Application
network	I-Application
.	O
</s>
<s>
The	O
reason	O
behind	O
the	O
choice	O
of	O
as	O
the	O
category	O
of	O
semantics	B-Application
is	O
that	O
vector	O
spaces	O
are	O
the	O
usual	O
setting	O
of	O
distributional	O
reading	O
in	O
computational	O
linguistics	O
and	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
<s>
Variations	O
of	O
DisCoCat	B-General_Concept
have	O
been	O
proposed	O
with	O
a	O
different	O
choice	O
for	O
the	O
grammar	O
category	O
.	O
</s>
<s>
The	O
DisCoCat	B-General_Concept
framework	O
has	O
been	O
used	O
to	O
study	O
the	O
following	O
phenomena	O
from	O
linguistics	O
.	O
</s>
<s>
The	O
DisCoCat	B-General_Concept
framework	O
has	O
been	O
applied	O
to	O
solve	O
the	O
following	O
tasks	O
in	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
