<s>
In	O
modal	O
logic	O
,	O
standard	B-Algorithm
translation	I-Algorithm
is	O
a	O
logic	O
translation	O
that	O
transforms	O
formulas	O
of	O
modal	O
logic	O
into	O
formulas	O
of	O
first-order	O
logic	O
which	O
capture	O
the	O
meaning	O
of	O
the	O
modal	O
formulas	O
.	O
</s>
<s>
Standard	B-Algorithm
translation	I-Algorithm
is	O
defined	O
inductively	O
on	O
the	O
structure	O
of	O
the	O
formula	O
.	O
</s>
<s>
In	O
short	O
,	O
atomic	B-Algorithm
formulas	I-Algorithm
are	O
mapped	O
onto	O
unary	O
predicates	B-Algorithm
and	O
the	O
objects	O
in	O
the	O
first-order	O
language	O
are	O
the	O
accessible	O
worlds	O
.	O
</s>
<s>
Standard	B-Algorithm
translation	I-Algorithm
is	O
defined	O
as	O
follows	O
:	O
</s>
<s>
,	O
where	O
is	O
an	O
atomic	B-Algorithm
formula	I-Algorithm
;	O
P(x )	O
is	O
true	O
when	O
holds	O
in	O
world	O
.	O
</s>
<s>
The	O
formula	O
holds	O
in	O
when	O
for	O
all	O
accessible	O
worlds	O
from	O
and	O
for	O
all	O
accessible	O
worlds	O
from	O
,	O
the	O
predicate	B-Algorithm
is	O
true	O
for	O
.	O
</s>
