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)?
If you think about each dissociate state separately, than it's easy to answer your question. $\ce{H2SO4}$ is a very strong acid $(\mathrm{p}K_\mathrm{a}\approx -3.0),$ but $\ce{HSO4-}$ is not so strong $(\mathrm{p}K_\mathrm{a}\approx 2.0).$

Phosphoric acid starts with $\mathrm{p}K_\mathrm{a}\approx 2.14,$ which as as you said is not so strong, and $\ce{H2PO4-}$ and $\ce{HPO4^2-}$ have $\mathrm{p}K_\mathrm{a}\approx 7.2$ and $\mathrm{p}K_\mathrm{a}\approx 12.3,$ so definetly weak.

So yes, we say sulfuric acid is strong because we're talking about $\ce{H2SO4},$ and what comes after should be mentioned separately.