A Formal Proof of Modal Completeness for Provability Logic

Authors Marco Maggesi , Cosimo Perini Brogi

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Marco Maggesi
  • University of Florence, Italy
Cosimo Perini Brogi
  • University of Genoa, Italy

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Marco Maggesi and Cosimo Perini Brogi. A Formal Proof of Modal Completeness for Provability Logic. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Higher order logic
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Automated reasoning
  • Provability Logic
  • Higher-Order Logic
  • Mechanized Mathematics
  • HOL Light Theorem Prover


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