Mathematical Institute, Zitna 25, 11000 Praha 1, Czech Republic, E-mail: email@example.com
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 ψ i must have a number of proof-lines exponential in terms of the size of ψ i . 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.
(Received May 24 2006)
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