<s>
Indeterminacy	B-Application
in	I-Application
concurrent	I-Application
computation	I-Application
is	O
concerned	O
with	O
the	O
effects	O
of	O
indeterminacy	B-Application
in	I-Application
concurrent	I-Application
computation	I-Application
.	O
</s>
<s>
Computation	O
is	O
an	O
area	O
in	O
which	O
indeterminacy	O
is	O
becoming	O
increasingly	O
important	O
because	O
of	O
the	O
massive	O
increase	O
in	O
concurrency	B-Architecture
due	O
to	O
networking	O
and	O
the	O
advent	O
of	O
many-core	B-Architecture
computer	O
architectures	O
.	O
</s>
<s>
which	O
he	O
attributed	O
to	O
Hayes	O
in	O
his	O
1988	O
paper	O
on	O
the	O
early	O
history	O
of	O
Prolog	B-Language
.	O
</s>
<s>
Contrary	O
to	O
Kowalski	O
and	O
Hayes	O
,	O
Carl	O
Hewitt	O
claimed	O
that	O
logical	O
deduction	O
was	O
incapable	O
of	O
carrying	O
out	O
concurrent	B-Architecture
computation	I-Architecture
in	O
open	O
systems	O
.	O
</s>
<s>
Hewitt	O
 [ 1985 ] 	O
and	O
Agha	O
[1991],	O
and	O
other	O
published	O
work	O
argued	O
that	O
mathematical	O
models	O
of	O
concurrency	B-Architecture
did	O
not	O
determine	O
particular	O
concurrent	B-Architecture
computations	I-Architecture
as	O
follows	O
:	O
The	O
Actor	B-Application
model	I-Application
makes	O
use	O
of	O
arbitration	O
(	O
often	O
in	O
the	O
form	O
of	O
notional	O
arbiters	O
)	O
for	O
determining	O
which	O
message	O
is	O
next	O
in	O
the	O
arrival	O
ordering	O
of	O
an	O
Actor	O
who	O
is	O
sent	O
multiple	O
messages	O
concurrently	O
.	O
</s>
<s>
Therefore	O
,	O
mathematical	O
logic	O
cannot	O
implement	O
concurrent	B-Architecture
computation	I-Architecture
in	O
open	O
systems	O
.	O
</s>
<s>
The	O
authors	O
claim	O
that	O
although	O
mathematical	O
logic	O
cannot	O
,	O
in	O
their	O
view	O
,	O
implement	O
general	O
concurrency	B-Architecture
it	O
can	O
implement	O
some	O
special	O
cases	O
of	O
concurrent	B-Architecture
computation	I-Architecture
,	O
e.g.	O
,	O
sequential	O
computation	O
and	O
some	O
kinds	O
of	O
parallel	B-Operating_System
computing	I-Operating_System
including	O
the	O
lambda	B-Language
calculus	I-Language
.	O
</s>
<s>
According	O
to	O
Hewitt	O
,	O
in	O
concrete	O
terms	O
for	O
Actor	B-Application
systems	I-Application
,	O
typically	O
we	O
cannot	O
observe	O
the	O
details	O
by	O
which	O
the	O
arrival	O
order	O
of	O
messages	O
for	O
an	O
Actor	O
is	O
determined	O
.	O
</s>
<s>
The	O
published	O
claim	O
was	O
that	O
because	O
of	O
the	O
indeterminacy	O
of	O
the	O
physical	O
basis	O
of	O
the	O
Actor	B-Application
model	I-Application
,	O
that	O
no	O
kind	O
of	O
deductive	O
mathematical	O
logic	O
could	O
escape	O
the	O
limitation	O
.	O
</s>
<s>
This	O
became	O
important	O
later	O
when	O
researchers	O
attempted	O
to	O
extend	O
Prolog	B-Language
(	O
which	O
had	O
some	O
basis	O
in	O
logic	B-Language
programming	I-Language
)	O
to	O
concurrent	B-Architecture
computation	I-Architecture
using	O
message	O
passing	O
.	O
</s>
<s>
Actor	B-Application
model	I-Application
theory	O
provides	O
the	O
means	O
to	O
characterize	O
all	O
the	O
possible	O
computations	O
of	O
a	O
closed	O
Actor	B-Application
system	I-Application
using	O
the	O
Representation	O
Theorem	O
[	O
Hewitt	O
2007 ]	O
as	O
follows	O
:	O
</s>
<s>
So	O
mathematical	O
logic	O
can	O
characterize	O
(	O
as	O
opposed	O
to	O
implement	O
)	O
all	O
the	O
possible	O
computations	O
of	O
a	O
closed	O
Actor	B-Application
system	I-Application
.	O
</s>
<s>
An	O
open	O
Actor	B-Application
system	I-Application
is	O
one	O
in	O
which	O
the	O
addresses	O
of	O
outside	O
Actors	O
can	O
be	O
passed	O
into	O
in	O
the	O
middle	O
of	O
computations	O
so	O
that	O
can	O
communicate	O
with	O
these	O
outside	O
Actors	O
.	O
</s>
<s>
When	O
other	O
models	O
of	O
concurrent	B-Operating_System
systems	O
(	O
e.g.	O
,	O
process	O
calculi	O
)	O
are	O
used	O
to	O
implement	O
open	O
systems	O
,	O
these	O
systems	O
also	O
can	O
have	O
behavior	O
that	O
depends	O
on	O
arrival	O
time	O
orderings	O
and	O
so	O
cannot	O
be	O
implemented	O
by	O
logical	O
deduction	O
.	O
</s>
<s>
developed	O
a	O
family	O
of	O
Prolog-like	O
concurrent	B-Operating_System
message	O
passing	O
systems	O
using	O
unification	O
of	O
shared	O
variables	O
and	O
data	O
structure	O
streams	O
for	O
messages	O
.	O
</s>
<s>
This	O
kind	O
of	O
system	O
was	O
used	O
as	O
the	O
basis	O
of	O
the	O
Japanese	O
Fifth	B-Device
Generation	I-Device
Project	I-Device
(	O
ICOT	O
)	O
.	O
</s>
<s>
Carl	O
Hewitt	O
and	O
Gul	O
Agha	O
 [ 1991 ] 	O
argued	O
that	O
these	O
Prolog-like	O
concurrent	B-Operating_System
systems	O
were	O
neither	O
deductive	O
nor	O
logical	O
:	O
like	O
the	O
Actor	B-Application
model	I-Application
,	O
the	O
Prolog-like	O
concurrent	B-Operating_System
systems	O
were	O
based	O
on	O
message	O
passing	O
and	O
consequently	O
were	O
subject	O
to	O
the	O
same	O
indeterminacy	O
.	O
</s>
<s>
Hewitt	O
maintained	O
that	O
a	O
basic	O
lesson	O
can	O
be	O
learned	O
from	O
Prolog	B-Language
and	O
the	O
Prolog-like	O
concurrent	B-Operating_System
systems	O
:	O
a	O
universal	O
model	O
of	O
concurrent	B-Architecture
computation	I-Architecture
is	O
limited	O
by	O
having	O
any	O
mandatory	O
overhead	O
in	O
the	O
basic	O
communication	O
mechanisms	O
.	O
</s>
<s>
But	O
compare	O
Shapiro	O
's	O
survey	O
of	O
Prolog-like	O
concurrent	B-Architecture
programming	I-Architecture
languages	O
for	O
arguments	O
for	O
inclusion	O
.	O
</s>
<s>
Arbitration	O
is	O
the	O
basis	O
of	O
the	O
indeterminacy	O
in	O
the	O
Actor	B-Application
model	I-Application
of	O
concurrent	B-Architecture
computation	I-Architecture
(	O
see	O
History	O
of	O
the	O
Actor	B-Application
model	I-Application
and	O
Actor	B-Application
model	I-Application
theory	O
)	O
.	O
</s>
<s>
It	O
may	O
also	O
play	O
a	O
role	O
in	O
other	O
models	O
of	O
concurrent	B-Operating_System
systems	O
,	O
such	O
as	O
process	O
calculi	O
.	O
</s>
