Dynamic Proof Theory for Dynamic Epistemic Logic

Abstract

This paper proposes a calculus for Dynamic Epistemic Logic (DEL) based on dynamic hypersequents, a new framework for capturing the dynamics of epistemic models in a purely structural and natural way. We enrich dynamic hypersequents with agent indices and an event store, yielding a uniform representation of epistemic events. The resulting calculus enjoys a set of logical rules that are provably invertible. Moreover, all structural rules, including the contraction rules, as well as the cut-rule, are shown to be admissible. Finally, the calculus constitutes, to the best of our knowledge, the only proof-theoretic calculus for DEL that is both grounded in a classical S5 framework and inherently dynamic.