Provability logic investigates the provability behavior of the mathematical theories. In a more precise way, it studies the relationship between a mathematical theory $T$ and a modal logic $L$ via the provability interpretation which interprets the modality as the provability predicate of $T$. In this talk we will extend this relationship to investigate the provability behavior of a hierarchy of theories. More precisely, using the modal language with infinite many modalities, $\{\Box_n\}_{n=0}^{\infty}$, we will define the hierarchical counterparts of some of the classical modal theories such as $\mathbf{K4}$, $\mathbf{KD4}$, $\mathbf{GL}$ and $\mathbf{S4}$. Then we will define their canonical provability interpretations and their corresponding soundness-completeness theorems.