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.
Multiple-conclusion rules, hypersequents syntax and step frames / N. Bezhanishvili, S. Ghilardi (ADVANCES IN MODAL LOGIC). - In: Advances in Modal Logic[s.l] : College Publications, 2014. - ISBN 9781848901513. - pp. 54-73 (( Intervento presentato al 10. convegno Conference on Advances in Modal Logic, AiML tenutosi a Groningen nel 2014.
Multiple-conclusion rules, hypersequents syntax and step frames
S. Ghilardi
2014
Abstract
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.File | Dimensione | Formato | |
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