There're variations of logical expressions. e.g.
$\forall a \exists b(P(a,b))$
is also written as
$\forall a \exists b:P(a,b)$
or
$\forall a \exists b.P(a,b)$
or even
$(\forall a \exists b)[P(a,b)]$
So I wonder if there is an official (or say well-accepted) formulation on logical expression forms.