Lower bounds for modal logics

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 1, 2, . . . s.t. every K-proof of i must have a number of proof-lines exponential in terms of the size of i . The result extends, for the same sequence of K-tautologies, to the systems K4, G¨odel-L¨ob’s logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.

• Type: Journal
• Year: 2007
• Where: JSYML
• Authors: Pavel Hrubes
• Keywords: Formulas, JSYML 2007, Lower Bound, Modal Logic