{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/towards-a-coq-formalization-of-a-quantified","title":"Towards a Coq formalization of a quantified modal logic","arxiv_id":"2206.03358","date":"2022-06-07","proceeding":null,"authors":["Ana de Almeida Borges"],"abstract":"We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The highlights are a deep embedding of $\\mathsf{QRC}_1$ in the Coq proof assistant, a mechanization of the notion of Kripke model with varying domains and a formalization of the soundness theorem. We focus on the design decisions inherent to the formalization and the insights that led to new and simplified proofs.","url_abs":"https://arxiv.org/abs/2206.03358v2","url_pdf":"https://arxiv.org/pdf/2206.03358v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"towards-a-coq-formalization-of-a-quantified","repo_url":"https://gitlab.com/ana-borges/QRC1-Coq","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}