Lower bounds for modal logics

Pavel Hrubeš
2007 Journal of Symbolic Logic (JSL)  
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 ψ i must have a number of proof-lines exponential in terms of the size of ψ i . The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel–Löb's logic, S andS4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.
doi:10.2178/jsl/1191333849 fatcat:5osv2td5ovgrzoijjzmaasrxja