Over the last years, the study of logics that can update a model while evaluating a formula has gained in interest. Motivated by many examples in practice such as hybrid logics, separation logics and dynamic epistemic logics, the ability to update a model has been investigated from a more general point of view. In this work, we formalize and verify in the proof assistant Coq, the bisimulation theorems for a particular family of dynamic logics that can change the structure of a relational model while evaluating a formula. Our framework covers update operators to perform different kinds of modifications on the accessibility relation, the valuation and the evaluation point of a model. The benefits of this formalization are twofold. First, our results apply for a wide variety of dynamic logics. Second, we argue that this is the first step towards the development of a modal logic library in Coq, which allows us to mechanize many relevant results.

在过去的几年中，对可以在评估公式的同时更新模型的逻辑的研究引起了人们的兴趣。在实践中，受许多示例（例如混合逻辑，分离逻辑和动态认知逻辑）的激励，已经从更广泛的角度研究了更新模型的能力。在这项工作中，我们在证明助手Coq中对特定的动态逻辑族的双仿真定理进行形式化和验证，可以在评估公式的同时更改关系模型的结构。我们的框架涵盖更新运算符，以对模型的可访问性关系，评估和评估点执行各种修改。这种形式化的好处是双重的。首先，我们的结果适用于各种各样的动态逻辑。第二，