Relational Hypersequents for Modal Logics

Samara Burns, Richard Zach

Published 2018-05-23Version 1

We investigate a new approach to modal hypersequents, called relational hypersequents, which incorporates an accessibility relation along the hypersequent. These systems are an adaptation of Restall's 2009 cut-free complete hypersequent system for S5. Variation between modal systems in the relational framework occurs only in the presence or absence of structural rules, which conforms to Do\v{s}en's principle. All systems are modular except for that of S5. We provide the first cut-free completeness result for K, T, and D, and show how this method fails in the case of B and S4.