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.
from cs updates on arXiv.org https://ift.tt/2s9bHIQ
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