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Multiple-conclusion rules, hypersequents syntax and step frames. (English) Zbl 1385.03016
GorĂ©, Rajeev (ed.) et al., Advances in modal logic. Vol. 10. Proceedings of the 10th conference (AiML 2014), Groningen, Netherlands, August 5–8, 2014. London: College Publications (ISBN 978-1-84890-151-3/pbk). 54-73 (2014).
Summary: We investigate proof theoretic properties of logical systems via algebraic methods. We introduce a calculus for deriving multiple-conclusion rules and show that it is a Hilbert style counterpart of hypersequent calculi. Using step-algebras we develop a criterion establishing the bounded proof property and finite model property for these systems. Finally, we show how this criterion can be applied to universal classes axiomatized by certain canonical rules, thus recovering and extending known results from both semantically and proof-theoretically inspired modal literature.
For the entire collection see [Zbl 1318.03006].

03B45 Modal logic (including the logic of norms)
03F07 Structure of proofs