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Syntactic Cut-Admissibility and Decidability

  • Francesca PoggiolesiEmail author
Chapter
Part of the Trends in Logic book series (TREN, volume 32)

Abstract

In Section 6.2 we proved that the weakening (internal and external) rules, the contraction rules, the rule of merge, the rule of necessitation and the special structural rules are all (height-preserving) admissible in the calculi Thsk \(^{*}_{L}\). These results are satisfactory both from a technical and from a conceptual point of view. The central question remains open: is the cut-rule admissible in the tree-hypersequent calculi? The answer is affirmative and it will be presented in the next section. More precisely, we will provide an algorithm for transforming derivations involving the cut-rule to derivations which are cut-free.

References

  1. 85.
    S. Negri. Proof analysis in modal logic. Journal of Philosophical Logic, 34:507–544, 2005.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.VRIJE UNIVERSITEIT BRUSSEL CLWF/LWBrusselsBelgium

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