General theory of cumulative inference
Proceedings of the 2nd international workshop on Non-monotonic reasoning
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
ACM Computing Surveys (CSUR)
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
Proof-complexity results for nonmonotonic reasoning
ACM Transactions on Computational Logic (TOCL)
Sequent calculi for propositional nonmonotonic logics
ACM Transactions on Computational Logic (TOCL)
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic reasoning: towards efficient calculi and implementations
Handbook of automated reasoning
Proof complexity of propositional default logic
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Proof complexity of non-classical logics
ESSLLI'10 Proceedings of the 2010 conference on ESSLLI 2010, and ESSLLI 2011 conference on Lectures on Logic and Computation
The complexity of theorem proving in autoepistemic logic
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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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.