In the present paper, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The displayapproach 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.
S. Frittella, G. Greco, A. Kurz, A. Palmigiano, and V. Sikimić, “Multi-type display calculus for dynamic epistemic logic,” Journal of Logic and Computation, vol. 26, no. 6, pp. 2017–2065, Dec. 2016. DOI: 10.1093/logcom/exu068
Oxford University Press