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3 results

  • Lower bounds to the size of constant-depth propositional proofs

  • Jan Krajíček
  • Journal:
    The Journal of Symbolic Logic / Volume 59 / Issue 1 / March 1994
    Published online by Cambridge University Press:
    12 March 2014, pp. 73-86
    Print publication:
    March 1994

  • LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and ∧,∨ (both of bounded arity). Then for every d ≥ 0 and n ≥ 2, there is a set of depth d sequents of total size O(n3+d) which are refutable in LK by depth d + 1 proof of size exp(O(log2n)) but such that every depth d refutation must have the size at least exp(nΩ(1)). The sets express a weaker form of the pigeonhole principle.