Geodesic
Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algorithmic aspects of algebra and logic, Tome 274 (2011), pp. 329-342

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We study interpolation properties of provability logics. We prove the Lyndon interpolation for $\mathbf{GL}$ and the uniform interpolation for $\mathbf{GLP}$. 
@article{TM_2011_274_a18,
     author = {Daniyar S. Shamkanov},
     title = {Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {329--342},
     publisher = {mathdoc},
     volume = {274},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_274_a18/}
}
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%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
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Daniyar S. Shamkanov. Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algorithmic aspects of algebra and logic, Tome 274 (2011), pp. 329-342. http://geodesic.mathdoc.fr/item/TM_2011_274_a18/