Geodesic
Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$
Informatics and Automation, Algorithmic aspects of algebra and logic, Tome 274 (2011), pp. 329-342.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study interpolation properties of provability logics. We prove the Lyndon interpolation for $\mathbf{GL}$ and the uniform interpolation for $\mathbf{GLP}$. 
@article{TRSPY_2011_274_a18,
     author = {Daniyar S. Shamkanov},
     title = {Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$},
     journal = {Informatics and Automation},
     pages = {329--342},
     publisher = {mathdoc},
     volume = {274},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_274_a18/}
}
TY  - JOUR
AU  - Daniyar S. Shamkanov
TI  - Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$
JO  - Informatics and Automation
PY  - 2011
SP  - 329
EP  - 342
VL  - 274
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2011_274_a18/
LA  - ru
ID  - TRSPY_2011_274_a18
ER  - 
%0 Journal Article
%A Daniyar S. Shamkanov
%T Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$
%J Informatics and Automation
%D 2011
%P 329-342
%V 274
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2011_274_a18/
%G ru
%F TRSPY_2011_274_a18
Daniyar S. Shamkanov. Interpolation properties for provability logics $\mathbf{GL}$ and $\mathbf{GLP}$. Informatics and Automation, Algorithmic aspects of algebra and logic, Tome 274 (2011), pp. 329-342. http://geodesic.mathdoc.fr/item/TRSPY_2011_274_a18/

[1] Artemov S.N., Beklemishev L.D., “Provability logic”, Handbook of philosophical logic, 13, 2nd ed., eds. D. Gabbay, F. Guenthner, Springer, Dordrecht, 2005, 189–360 | DOI

[2] Beklemishev L.D., “Kripke semantics for provability logic GLP”, Ann. Pure and Appl. Logic., 161 (2010), 756–774 | DOI | MR | Zbl

[3] Beklemishev L.D., “On the Craig interpolation and the fixed point property for GLP”, Proofs, categories and computations, Essays in honor of G. Mints, Tributes, 13, eds. S. Feferman, W. Sieg, College Publ., London, 2010, 49–60 | Zbl

[4] Beklemishev L.D., “Uproschennoe dokazatelstvo teoremy ob arifmeticheskoi polnote dlya logiki dokazuemosti $\mathbf {GLP}$”, Tr. MIAN, 274 (2011), 32–40 | Zbl

[5] Boolos G., The unprovability of consistency: An essay in modal logic, Cambridge Univ. Press, Cambridge, 1979 | MR | Zbl

[6] D'Agostino G., “Uniform interpolation, bisimulation quantifiers, and fixed points”, Logic, language, and computation, Proc. 6th Intern. Tbilisi Symp. TbiLLC 2005, Batumi (Georgia), Sept. 2005, Lect. Notes Comput. Sci., 4363, eds. B.D. ten Cate, H.W. Zeevat, Springer, Berlin, 2007, 96–116 | DOI | Zbl

[7] D'Agostino G., Hollenberg M., “Logical questions concerning the $\mu $-calculus: Interpolation, Lyndon and Łoś-Tarski”, J. Symb. Log., 65:1 (2000), 310–332 | DOI | MR | Zbl

[8] Ghilardi S., Zawadowski M., “A sheaf representation and duality for finitely presented Heyting algebras”, J. Symb. Log., 60:3 (1995), 911–939 | DOI | MR | Zbl

[9] Goranko V., Otto M., “Model theory of modal logic”, Handbook of modal logic, eds. P. Blackburn, J. van Benthem, F. Wolter, Elsevier, Amsterdam, 2007, 249–329 | DOI

[10] Ignatiev K.N., “On strong provability predicates and the associated modal logics”, J. Symb. Log., 58:1 (1993), 249–290 | DOI | MR | Zbl

[11] Dzhaparidze G.K., Modalno-logicheskie sredstva issledovaniya dokazuemosti, Dis. ... kand. filos. nauk, MGU, M., 1986

[12] Pitts A.M., “On an interpretation of second order quantification in first order intuitionistic propositional logic”, J. Symb. Log., 57:1 (1992), 33–52 | DOI | MR | Zbl

[13] Shavrukov V.Yu., Subalgebras of diagonalizable algebras of theories containing arithmetic, Diss. math., 323, Inst. Mat., Pol. Acad. Sci., Warszawa, 1993 | MR

[14] Smoryński C., “Beth's theorem and self-referential sentences”, Logic colloquium '77, Proc. Colloq., Wrocław, 1977, eds. A. Macintyre, L. Pacholski, J. Paris, North-Holland, Amsterdam, 1978, 253–261 | DOI | MR

[15] van Benthem J., “Modal frame correspondences and fixed-points”, Stud. log., 83:1–3 (2006), 133–155 | MR | Zbl

[16] Visser A., “Uniform interpolation and layered bisimulation”, Gödel '96. Logical foundations of mathematics, computer science and physics—Kurt Gödel's legacy, Proc. Conf., Brno (Czech Rep.), Aug. 1996, Lect. Notes Log., 6, eds. P. Hájek, Springer, Berlin, 1996, 139–164 | DOI | MR | Zbl