Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
Is Non-Monotonic Reasoning Always Harder?
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Non-elementary Speed-Ups in Default Reasoning
ECSQARU/FAPR '97 Proceedings of the First International Joint Conference on Qualitative and Quantitative Practical Reasoning
Sequent Calculi for Default and Autoepistemic Logics
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Tableau Calculus for Minimal Model Reasoning
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
A Sequent Calculus for Skeptical Default Logic
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Sequent Calculus for Circumscription
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Proof-complexity results for nonmonotonic reasoning
ACM Transactions on Computational Logic (TOCL)
Sequent calculi for propositional nonmonotonic logics
ACM Transactions on Computational Logic (TOCL)
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Circumscription is a non-monotonic formalism based on the idea that objects satisfying a certain predicate expression are considered as the only objects satisfying it. Theoretical complexity results imply that circumscription is (in the worst case) computationally harder than classical logic. This somehow contradicts our intuition about commonsense reasoning: non-monotonic rules should help to speed up the reasoning process, and not to slow it down.In this paper, we consider a first-order sequent calculus for circumscription and show that the presence of circumscription rules can tremendously simplify the search for proofs. In particular, we show that certain sequents have only long "classical" proofs, but short proofs can be obtained by using circumscription.