Relational Hypersequents for Modal Logics

05/23/2018

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by   Samara Burns, et al.

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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 Došen'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.