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arXiv · 2206.03358

Towards a Coq formalization of a quantified modal logic

Ana de Almeida Borges
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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.

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Ana de Almeida Borges. 2022-06-07. Towards a Coq formalization of a quantified modal logic. https://arxiv.org/abs/2206.03358

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