Archive for Mathematical Logic

, Volume 50, Issue 7–8, pp 727–742 | Cite as

Proof complexity of propositional default logic

  • Olaf BeyersdorffEmail author
  • Arne Meier
  • Sebastian Müller
  • Michael Thomas
  • Heribert Vollmer


Default logic is one of the most popular and successful formalisms for non-monotonic reasoning. In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic. In this paper we examine these calculi from a proof-complexity perspective. In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen’s system LK. Hence proving lower bounds for credulous reasoning will be as hard as proving lower bounds for LK. On the other hand, we show an exponential lower bound to the proof size in Bonatti and Olivetti’s enhanced calculus for skeptical default reasoning.


Default logic Sequent calculus Proof complexity 

Mathematics Subject Classification (2000)

03F20 03B60 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Olaf Beyersdorff
    • 1
    Email author
  • Arne Meier
    • 1
  • Sebastian Müller
    • 2
  • Michael Thomas
    • 1
  • Heribert Vollmer
    • 1
  1. 1.Institute of Theoretical Computer ScienceLeibniz University HanoverHanoverGermany
  2. 2.Faculty of Mathematics and PhysicsCharles University PraguePragueCzech Republic

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