aqueous solution - Confused about strong/weak dibasic and tribasic acids

I know that sulfuric acid is considered a strong acid, and the dissociation of its first $\ce{H+}$ ion is complete and of its second $\ce{H+}$ ion is partial.

Phosphoric acid is weak and all three of its $\ce{H+}$ ions dissociate partially.

I just wanted to clarify: are dibasic and tribasic acids considered strong if their first dissociation is complete (and subsequent ones will naturally be partial)?

Answer

I mean whenever you have a polyprotic acid/base and they say that if it is strong or weak you can only assume the first dissociation is strong or weak.

Say like you have $\ce{H2SO4}$ and we all know that it is a strong acid. This only means that the first dissociation is strong.

$$\ce{H2SO4 -> HSO4- + H3O+}$$

So in this case above only the first dissociation is strong. And then you cannot and do not know if $\ce{HSO4}$ is strong as well.

So overall in any case we cannot assume and the data must be provided. Good Question.