If there is an official (or say well-accepted) formulation on logical expression forms?

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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.