Multi-type display calculus for dynamic epistemic logic

In the present article, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The display approach is suitable to modularly chart the space of dynamic epistemic logics on weaker-than-classical propositional base. The presence of types endows the language of the Dynamic Calculus with additional expressivity, allows for a smooth proof-theoretic treatment, and paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag–Moss–Solecki's dynamic epistemic logic, and enjoys Belnap-style cut elimination.