Global Neighbourhood Completeness of the Gödel-Löb Provability Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10388)

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.

Keywords

Provability logic Neighbourhood semantics Global consequence relations Non-well-founded proofs 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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