Verification of dynamic bisimulation theorems in Coq

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.