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Lower bounds for modal logics

Published online by Cambridge University Press:  12 March 2014

Pavel Hrubeš
Pavel Hrubeš*
Affiliation:
Mathematical Institute, Zitna 25, 11000 Praha 1, Czech Republic, E-mail: pahrubes@centrum.cz
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Abstract

We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ1, ψ2, … s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel–Löb's logic, S andS4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.

Keywords

Proof complexitymodal logiclower boundmonotone interpolation
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 941 - 958
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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