Contains/element-of are the complementary formal verbs from set theory, but I’ve definitely seen Contains/is-a used as equivalent in practice (cats contains Garfield because Garfield is a cat).
Similarly in programming “cat is Garfield’s type” makes sense although it’s verbose, or “cat is implemented by Garfield” for the traits folks which is far more natural.
So where linguistically necessary humans have had no trouble complementing is-a in natural language. I think it’s a matter of where emphasis is desired; usually the subject (Garfield) is where the emphasis is, and usually the element is the subject instead of the class. Formally we often want the class/set/type to be the subject since it’s the thing we are emphasizing.
Contains/element-of are the complementary formal verbs from set theory, but I’ve definitely seen Contains/is-a used as equivalent in practice (cats contains Garfield because Garfield is a cat).
Similarly in programming “cat is Garfield’s type” makes sense although it’s verbose, or “cat is implemented by Garfield” for the traits folks which is far more natural.
So where linguistically necessary humans have had no trouble complementing is-a in natural language. I think it’s a matter of where emphasis is desired; usually the subject (Garfield) is where the emphasis is, and usually the element is the subject instead of the class. Formally we often want the class/set/type to be the subject since it’s the thing we are emphasizing.