Towards a Coq formalization of a quantified modal logic

06/07/2022

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by   Ana de Almeida Borges, et al.

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We present a Coq formalization of the Quantified Reflection Calculus with one modality, or 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 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.