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Mat. Zametki, 2012, Volume 91, Issue 3, Pages 331–346 (Mi mz9138)  

This article is cited in 11 scientific papers (total in 11 papers)

On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$

E. V. Dashkov

M. V. Lomonosov Moscow State University

Abstract: 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 $\mathbf{GLP}$, equational calculus, deductive system, Kripke semantics, complexity of a decision procedure

DOI: https://doi.org/10.4213/mzm9138

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English version:
Mathematical Notes, 2012, 91:3, 318–333

Bibliographic databases:

UDC: 510
Received: 24.04.2011
Revised: 17.07.2011

Citation: E. V. Dashkov, “On the Positive Fragment of the Polymodal Provability Logic $\mathbf{GLP}$”, Mat. Zametki, 91:3 (2012), 331–346; Math. Notes, 91:3 (2012), 318–333

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. Beklemishev, “Positive provability logic for uniform reflection principles”, Ann. Pure Appl. Log., 165:1 (2014), 82–105  crossref  mathscinet  zmath  isi  elib  scopus
    2. L. D. Beklemishev, D. Fernández-Duque, J. J. Joosten, “On provability logics with linearly ordered modalities”, Stud. Log., 102:3 (2014), 541–566  crossref  mathscinet  zmath  isi  scopus
    3. D. Fernández-Duque, J. J. Joosten, “Well-orders in the transfinite Japaridze algebra”, Log. J. IGPL, 22:6 (2014), 933–963  crossref  mathscinet  isi  scopus
    4. F. Pakhomov, “On the complexity of the closed fragment of Japaridze's provability logic”, Arch. Math. Log., 53:7-8 (2014), 949–967  crossref  mathscinet  zmath  isi  scopus
    5. L. D. Beklemishev, “On the reflection calculus with partial conservativity operators”, Logic, Language, Information, and Computation: 24Th International Workshop, Wollic 2017, London, UK, July 18-21, 2017, Proceedings, Lecture Notes in Computer Science, 10388, eds. J. Kennedy, R. de Queiroz, Springer International Publishing Ag, 2017, 48–67  crossref  mathscinet  zmath  isi  scopus
    6. Fernandez-Duque D., “The Intuitionistic Temporal Logic of Dynamical Systems”, Log. Meth. Comput. Sci., 14:3 (2018), 3  crossref  zmath  isi
    7. M. V. Svyatlovskiy, “Axiomatization and Polynomial Solvability of Strictly Positive Fragments of Certain Modal Logics”, Math. Notes, 103:6 (2018), 952–967  mathnet  crossref  crossref  isi  elib
    8. L. D. Beklemishev, “Reflection calculus and conservativity spectra”, Russian Math. Surveys, 73:4 (2018), 569–613  mathnet  crossref  crossref  adsnasa  isi  elib
    9. Beklemishev L., “A Note on Strictly Positive Logics and Word Rewriting Systems”, Larisa Maksimova on Implication, Interpolation, and Definability, Outstanding Contributions to Logic, 15, ed. Odintsov S., Springer, 2018, 61–70  crossref  mathscinet  isi
    10. Berger G., Beklemishev L.D., Tompits H., “A Many-Sorted Variant of Japaridze'S Polymodal Provability Logic”, Log. J. IGPL, 26:5 (2018), 505–538  crossref  mathscinet  isi  scopus
    11. Kikot S., Kurucz A., Tanaka Y., Wolter F., Zakharyaschev M., “Kripke Completeness of Strictly Positive Modal Logics Over Meet-Semilattices With Operators”, J. Symb. Log., 84:2 (2019), 533–588  crossref  isi
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