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Equivalence of Agents
The Expansion Law
The Expansion Law
Let
P
<=>
(P
1
[f
1
] | ...| P
n
[f
n
])
\
L
P
=
sum
{
f
1
(
alpha
).(P
1
[f
1
] | ...| P
i
'[f
i
] | ...| P
n
[f
n
]
)\
L
:
P
i
->
alpha
P
i
'
,
f
i
(
alpha
) not in
L
union
L
}
+
sum
{
tau
.(
P
1
[f
1
] | ...| P
i
'[f
i
] | ...| P
j
'[f
j
] | ...| P
n
[f
n
]
)\
L
:
P
i
->
l_1
P
i
'
,
P
j
->
l_2
P
j
'
,
f
i
(
l
1
) =
f
i
(l
2
)
,
i < j
}
Corollary
Let
P
<=>
(P
1
| ...| P
n
)
\
L
P
=
sum
{
alpha
.(
P
1
| ...| P
i
' | ...| P
n
)\
L
:
P
i
->
alpha
P
i
'
,
alpha
not in
L
union
L'
}
+
sum
{
tau
.(
P
1
| ...| P
i
' | ...| P
j
' | ...P
n
)\
L
:
P
i
->
l
P
i
'
,
P
j
->
l
P
j
'
,
i < j
}
Example
P
1
=
a.P
1
' + b.P
1
"
P
2
=
a
.
P
2
' + c.P
2
"
(
P
1
|P
2
)\
a
=
b.(P
1
"|P
2
)
\
a
+
c.(P
1
|P
2
")
\
a
+
tau
.
(P
1
'|P
2
')
\
a
Author:
Wolfgang Schreiner
Last Modification: June 8, 1998
