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Coq formalization of QRC1

de Almeida Borges, Ana

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.

v0.1.0 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 proof of the Lindenbaum Lemma for QRC1; and
  • a proof of the Pair Existence Lemma for QRC1.
The code can also be found on GitLab at https://gitlab.com/ana-borges/QRC1-Coq/-/releases/v0.1.0
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  • 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

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