[robjan]

I think the key words are "a" vs "the" when you use "a" the relationship is one to many, whereas when you use "the" it's one to one. If I say "Charles is the King" then "the King is Charles" also holds true. If I say "Charles is a King" then I can't conclude that the King is Charles.

[beardyw]

So "dogs are animals", does that work?

[diffeomorphism]

Yes, "dogs are the animals (e.g. the only animals on this space station)" is implied to be reversible. Indefinite or missing articles like in your example make no such implication.