logic – Visualize Users Group Selection and Intersection

Your statements are complex because they contain a lot of information

Yes, natural language makes it easier to read, but it does not help with processing the 5 elements (desktop, mobile,…) and relations in one sentence. It is up to you to restrict the user to a more simple version of this, so it will be easier to comprehend. Look at email filters, for example (see image below).

Some relations cannot be expressed in natural language

For example, it is not clear to me if your statement includes Desktop users per-se or both desktop and mobile users have to belong to a group.

Desktop AND (Mobile users who belong to ...) or
Desktop AND Mobile who belong to ...