The purpose of this paper is to present a formalization of the language, semantics and axiomatization of justification logic in Coq. We present proofs in a natural deduction style derived from the axiomatic approach of justification logic. Additionally, we present possible world semantics in Coq based on Fitting models to formalize the semantic satisfaction of formulas. As an important result, with this implementation, it is possible to give a proof of soundness for |$\mathsf{L}\mathsf{P}$| with respect to Fitting models.

中文翻译：

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证明助手Coq中证明逻辑的自然推论和语义模型

本文的目的是提出Coq中语言的形式化，语义逻辑和证明逻辑的公理化。我们以一种自然推论的方式提出证明，这种推论是从证明逻辑的公理方法得出的。此外，我们基于拟合模型在Coq中展示可能的世界语义，以形式化公式的语义满意度。重要的结果是，通过此实现，可以为| $ \ mathsf {L} \ mathsf {P} $ |提供合理的证明。关于拟合模型。