Journal of Symbolic Logic

Lower bounds for modal logics

Pavel Hrubeš

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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 ψ12,… 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.

Article information

J. Symbolic Logic, Volume 72, Issue 3 (2007), 941-958.

First available in Project Euclid: 2 October 2007

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Zentralblatt MATH identifier

Proof complexity modal logic lower bound monotone interpolation


Hrubeš, Pavel. Lower bounds for modal logics. J. Symbolic Logic 72 (2007), no. 3, 941--958. doi:10.2178/jsl/1191333849.

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