Only skimmed this and didn't read the underlying paper, but I was surprised to see no mention of the fact that "A is B" often does not at all imply "B is A" in everyday language: A bird is an animal, but it's wrong to conclude that an arbitrary animal must be a bird.
However, you are right that it's not always correct since "Poetry is Literature" and "Steam/Ice is H20" are both examples where this breaks down.
My annoying pedantry for the day.