Source: J. Symbolic Logic
Volume 72, Issue 3
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 and S4. We also determine
some speed-up relations between different systems of modal logic on formulas of
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