  We study interpolation properties for Shavrukov's bimodal logic $\mathbf{GR}$
of usual and Rosser provability predicates. For this purpose, we introduce a
new sublogic $\mathbf{GR}^\circ$ of $\mathbf{GR}$ and its relational semantics.
Based on our new semantics, we prove that $\mathbf{GR}^\circ$ and $\mathbf{GR}$
enjoy Lyndon interpolation property and uniform interpolation property.
