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"The system mailbox can be accessed by everyone in the group if the file system is locked".

The doubt is how to represent the part 'the file system is locked'. There is only one file system, so I was thinking of using ∀x Locked(x), where x belongs to the domain of all file systems. Is this approach correct?

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    I think it makes more sense to introduce a constant (say, $f$) for the file system, since it appears there is only one file system in the universe of discourse anyway (*the* filesystem). Edit: but to be clear, if there is indeed only one file system then your statement is equivalent. – 2017-02-18

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As Mees de Vries says, it makes sense to name the file system. I interpret your sentence as follows.

Let $L(v)$ be the unary predicate "v is locked", let $f$ name the file system, let $G(x)$ be the unary predicate "x is a member of the group", let $A(v_1, v_2)$ be the binary predicate "$v_1$ has access to $v_2$", and let $m$ name the mailbox. Then,

$$L(f) \to (\forall x (G(x) \to A(x,m))).$$

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    Can't we simply use L (denoting 'the file system is locked')? i.e. a simple proposition will do there right? – 2017-02-18
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    I suppose it depends on your language. What are the atomic sentences? Typically, in first order languages, atomic sentences are of the form $P(a_1,...,a_n)$, where $P$ is a predicate and $a_1,...,a_n$ are constants. You can add atomic sentence symbols to the language, like $L$ in your suggestion. But using them for translations is not really in the spirit of the exercise. Extending your suggestion, we could just translate the entire conditional sentence using an atom $A$! The goal with these exercises is to capture as much sentential structure as possible, so $L(f)$ is preferable. – 2017-02-18