The expressivity hierarchy conjecture for finitely iterated supervenience languages

Let $\mathcal{L}_{\Rrightarrow^n}$ be the propositional language with the $n$-ary supervenience operator $\Rrightarrow^n$.

Expressivity hierarchy conjecture. For all $n\in\mathbb{N}$, $\mathcal{L}_{\Rrightarrow^{n+1}}$ is more expressive than $\mathcal{L}_{\Rrightarrow^n}$.

The paper establishes the corresponding result for $n=0$ and leaves the generalization to future work.