Formal space

A space is formal over $\mathbb{Q}$ if its rational cochain commutative differential graded algebra is joined to $(H^{\ast }(X;\mathbb{Q}),0)$ by quasi-isomorphisms. Equivalently in the usual simply connected Sullivan-model setting, its minimal model has a quasi-isomorphism to its cohomology algebra with zero differential. This says its rational homotopy type can be recovered from the cohomology algebra; zero cup products alone do not imply formality of a topological space without an additional argument.