In your case, dogs are only those animals that bark. That's a subset of animal. Think of it this way: can you think of an object that satisfies (is-a) Dog, but

In your case, dogs are only those animals that bark. That's a subset of animal. Think of it this way: can you think of an object that satisfies (is-a) Dog, but not Animal? No. Can you think of an object that satisfies Animal, but not Dog? Yes. So Dog ⊂ Animal. hbrn has it right calling those properties constraints, not features. With anything but a sealed class, the properties that are not present are unspecified rather than missing. And indeed sealed classes feel very "un-set-theoretic" to me.