Journal of Symbolic Logic

Lower bounds for modal logics

Pavel Hrubeš

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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 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

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

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333849

Digital Object Identifier
doi:10.2178/jsl/1191333849

Mathematical Reviews number (MathSciNet)
MR2354908

Zentralblatt MATH identifier
1125.03043

Keywords
Proof complexity modal logic lower bound monotone interpolation

Citation

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


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