Geodesic
On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$
Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 331-346.

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The fragment of the polymodal provability logic $\mathbf{GLP}$ in the language with connectives $\top$, $\wedge$, and $\langle n\rangle$ for all $n\in\omega$ is considered. For this fragment, a deductive system it constructed, a Kripke semantics is proposed, and a polynomial bound for the complexity of a decision procedure is obtained.
Keywords: modal logic, graded provability logic $\mathbf{GLP}$, deductive system, Kripke semantics, complexity of a decision procedure.
Mots-clés : equational calculus 
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E. V. Dashkov. On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$. Matematičeskie zametki, Tome 91 (2012) no. 3, pp. 331-346. http://geodesic.mathdoc.fr/item/MZM_2012_91_3_a1/

[1] L. D. Beklemishev, “Provability algebras and proof-theoretic ordinals, I”, Ann. Pure Appl. Logic, 128:1-3 (2004), 103–123 | DOI | MR | Zbl

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

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

[4] L. D. Beklemishev, “The Worm Principle”, Logic Colloquium '02, Lect. Notes Log., 27, Assoc. Symbol. Logic, La Jolla, CA, 2006, 75–95 | MR | Zbl

[5] I. Shapirovsky, “PSPACE-decidability of Japaridze's polymodal logic”, Advances in Modal Logic, Vol. 7, College Publ., London, 2008, 289–304 | MR | Zbl

[6] J. Dunn, “Positive modal logic”, Studia Logica, 55:2 (1995), 301–317 | DOI | MR | Zbl

[7] S. Celani, R. Jansana, “A new semantics for positive modal logic”, Notre Dame J. Formal Logic, 38:1 (1997), 1–18 | DOI | MR | Zbl

[8] F. Baader, S. Brandt, C. Lutz, “Pushing the $\mathcal{EL}$ envelope”, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence IJCAI-05, Morgan-Kaufmann Publ., Edinburgh, 2005, 364–369

[9] F. Baader, S. Brandt, C. Lutz, “Pushing the $\mathcal{EL}$ envelope further”, Proceedings of the OWLED 2008 DC Workshop on OWL: Experiences and Directions, 2008

[10] A. Kurucz, F. Wolter, M. Zakharyaschev, “Islands of tractability for relational constraints: towards dichotomy results for the description logic $\mathcal{EL}$”, Advances in Modal Logic, Vol. 8, College Publ., London, 2010, 271–291

[11] V. Sofronie-Stokkermans, “Locality and subsumption testing in $\mathcal{EL}$ and some of its extensions”, Advances in Modal Logic, Vol. 7, College Publ., London, 2008, 315–339 | MR | Zbl

[12] L. D. Beklemishev, J. J. Joosten, M. Vervoort, “A finitary treatment of the closed fragment of Japaridze's provability logic”, J. Logic Comput., 15:4 (2005), 447–463 | DOI | MR | Zbl

[13] L. D. Beklemishev, “Kripke semantics for provability logic GLP”, Ann. Pure Appl. Logic, 161:6 (2010), 756–774 | DOI | MR | Zbl

[14] A. Chagrov, M. Zakharyaschev, Modal Logic, Oxford Logic Guides, 35, Clarendon Press, Oxford, 1997 | MR | Zbl