Lower bounds for modal logics
Pavel Hrubeš
Source: J. Symbolic Logic Volume 72, Issue 3
(2007), 941-958.
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 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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1191333849
Digital Object Identifier: doi:10.2178/jsl/1191333849
Mathematical Reviews number (MathSciNet): MR2354908
Zentralblatt MATH identifier: 1125.03043
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