Lower Bounds for Modal Logics

Journal of Symbolic Logic 72 (3):941 - 958 (2007)
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 modal-depth one
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DOI 10.2178/jsl/1191333849
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Pavel Hrubeš (2009). On Lengths of Proofs in Non-Classical Logics. Annals of Pure and Applied Logic 157 (2):194-205.
Samuel R. Buss (2012). Towards–Via Proof Complexity and Search. Annals of Pure and Applied Logic 163 (7):906-917.

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