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Global Neighbourhood Completeness of the Gödel-Löb Provability Logic

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Logic, Language, Information, and Computation (WoLLIC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10388))

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Abstract

The Gödel-Löb provability logic \(\mathsf {GL}\) is strongly neighbourhood complete in the case of the so-called local semantic consequence relation. In the given paper, we consider Hilbert-style non-well-founded derivations in \(\mathsf {GL}\) and establish that \(\mathsf {GL}\) with the obtained derivability relation is strongly neighbourhood complete in the case of the global semantic consequence relation.

This work was supported by the Russian Science Foundation (grant no. 14-50-00005).

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Acknowledgements

The development of main ideas of this paper took place during my stay in Tash-Bulak village, the Kyrgyz Republic, in 2015. I heartily thank my uncle Kengebek Shamkanov and his family for their hospitality. In addition, I am grateful to Tadeusz Litak, whose constructive comments have helped me to improve the manuscript.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia

    Daniyar Shamkanov

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  1. Daniyar Shamkanov
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Correspondence to Daniyar Shamkanov .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Juliette Kennedy

  2. Centro de Informática, Recife, Pernambuco, Brazil

    Ruy J.G.B. de Queiroz

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Shamkanov, D. (2017). Global Neighbourhood Completeness of the Gödel-Löb Provability Logic. In: Kennedy, J., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2017. Lecture Notes in Computer Science(), vol 10388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55386-2_26

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  • DOI: https://doi.org/10.1007/978-3-662-55386-2_26

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  • Print ISBN: 978-3-662-55385-5

  • Online ISBN: 978-3-662-55386-2

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