Published July 5, 2023 | Version 1.0.0
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Coq formalization of QRC1

Creators

  • 1. University of Barcelona

Description

This is a Coq formalization of the QRC1 quantified modal logic introduced in Quantified Reflection Calculus with one modality and further studied in An Escape from Vardanyan’s Theorem. Part of the Coq formalization is described in Towards a Coq formalization of a quantified modal logic.

v1.0.0 includes:

  • the syntax of quantified and strictly positive formulas
  • the notion of QRC1 proof
  • a proof that it is possible to conservatively add extra constants to the language
  • the notion of Kripke model for QRC1
  • a proof of Kripke soundness for QRC1
  • a (non-constructive) proof of Kripke completeness for QRC1
  • a (non-constructive) proof of decidability for QRC1

The main changes when compared with v0.1.0 are the full Kripke completeness proof and the addition of the decidability proof.

Notes

The code can also be found on GitLab at https://gitlab.com/ana-borges/QRC1-Coq/-/releases/v1.0.0

Files

QRC1-Coq-v1.0.0.zip

Files (11.8 MB)

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Additional details

References

  • A. A. Borges, and J. J. Joosten (2020). Quantified Reflection Calculus with one modality. Advances in Modal Logic 13: 13-32.
  • A. A. Borges, and J. J. Joosten (2022). An Escape from Vardanyan's Theorem. Journal of Symbolic Logic. DOI: 10.1017/jsl.2022.38
  • A. A. Borges (2022). Towards a Coq formalization of a quantified modal logic. Proceedings of the 4th Workshop on Automated Reasoning in Quantified Non-Classical Logics (ARQNL 2022): 13-27