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URN: urn:nbn:de:0030-drops-139215
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A Formal Proof of Modal Completeness for Provability Logic

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Abstract

This work presents a formalized proof of modal completeness for Gödel-Löb provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation. In particular, we show how we adapted the proof in the Boolos' monograph according to the formal language and tools at hand. The strategy we develop here overcomes the technical difficulty due to the non-compactness of GL, and simplify the implementation. Moreover, it can be applied to other normal modal systems with minimal changes.

BibTeX - Entry

@InProceedings{maggesi_et_al:LIPIcs.ITP.2021.26,
  author =	{Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Formal Proof of Modal Completeness for Provability Logic}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13921},
  URN =		{urn:nbn:de:0030-drops-139215},
  doi =		{10.4230/LIPIcs.ITP.2021.26},
  annote =	{Keywords: Provability Logic, Higher-Order Logic, Mechanized Mathematics, HOL Light Theorem Prover}
}

Keywords: Provability Logic, Higher-Order Logic, Mechanized Mathematics, HOL Light Theorem Prover
Seminar: 12th International Conference on Interactive Theorem Proving (ITP 2021)
Issue date: 2021
Date of publication: 21.06.2021
Supplementary Material: The implementation described in this paper is hosted in the subdirectory GL of the distribution of https://www.cl.cam.ac.uk/~jrh13/hol-light/.
Software (HOL Light source code): https://github.com/jrh13/hol-light/ archived at: https://archive.softwareheritage.org/swh:1:dir:288139a46b5250ca678d928a823173f4f69c8594


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