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September 2007 Lower bounds for modal logics
Pavel Hrubeš
J. Symbolic Logic 72(3): 941-958 (September 2007). DOI: 10.2178/jsl/1191333849

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.

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Pavel Hrubeš. "Lower bounds for modal logics." J. Symbolic Logic 72 (3) 941 - 958, September 2007. https://doi.org/10.2178/jsl/1191333849

Information

Published: September 2007
First available in Project Euclid: 2 October 2007

zbMATH: 1125.03043
MathSciNet: MR2354908
Digital Object Identifier: 10.2178/jsl/1191333849

Keywords: lower bound , modal logic , monotone interpolation , Proof complexity

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 3 • September 2007
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