Can someone please help me formally translate the sentence "it is impossible for x to exist without y existing as well" into modal logic using ~◇? Or, similarly, the sentence "it is impossible for both x to be the case and not y to be the case." Thank you.

  • Do you have a predicate ‘E’ expressing ‘actually exists’ ? Jul 4, 2018 at 8:19
  • No but what would that look like?
    – user34064
    Jul 4, 2018 at 8:42

1 Answer 1


I assume that we can treat x and y as constants (i.e. "names") :

~◊ (∃z(z=x) & ~∃w(w=y)).

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