Proof Complexity of Propositional Default Logic

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.