A way to communicate Exists(N) and not Exists(S) in a way that doesn’t depend on the context of the current conversation might be “”Santa” exists but Santa does not.” Of course, the existence of “Santa” is granted when “Santa does not exist” is understood by the other person, so this is really just a slightly less ambiguous way of saying “Santa does not exist”
A way to communicate Exists(N) and not Exists(S) in a way that doesn’t depend on the context of the current conversation might be “”Santa” exists but Santa does not.” Of course, the existence of “Santa” is granted when “Santa does not exist” is understood by the other person, so this is really just a slightly less ambiguous way of saying “Santa does not exist”
Slightly.