A generalization of collapsible cases of circumscription
Artificial Intelligence
General theory of cumulative inference
Proceedings of the 2nd international workshop on Non-monotonic reasoning
All I know: a study in autoepistemic logic
Artificial Intelligence
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
Arithmetic classification of perfect models of stratified programs
Fundamenta Informaticae
Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
What does a conditional knowledge base entail?
Artificial Intelligence
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
On the decidability and complexity of autoepistemic reasoning
Fundamenta Informaticae - Special issue on modal logics in knowledge representation
Default reasoning using classical logic
Artificial Intelligence
On different structure-preserving translations to normal form
Journal of Symbolic Computation
Is intractability of nonmonotonic reasoning a real drawback?
Artificial Intelligence
The resolution calculus
On compact representations of propositional circumscription
Theoretical Computer Science
Theorem Proving via General Matings
Journal of the ACM (JACM)
Tractable Reasoning in Artificial Intelligence
Tractable Reasoning in Artificial Intelligence
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
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
On Proof Complexity of Circumscription
TABLEAUX '98 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
An Extended Framework for Default Reasoning
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
Nonmonotonic reasoning: towards efficient calculi and implementations
Handbook of automated reasoning
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
A survey on knowledge compilation
AI Communications
The comparative linguistics of knowledge representation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
On polynomial sized MDP succinct policies
Journal of Artificial Intelligence Research
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Proof complexity of propositional default logic
Archive for Mathematical Logic
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
| Hi-index | 0.00 |
It is well-known that almost all nonmonotonic formalisms have a higher worst-case complexity than classical reasoning. In some sense, this observation denies one of the original motivations of nonmonotonic systems, which was the expectation taht nonmonotonic rules should help to speed-up the reasoning process, and not make it more difficult. In this paper, we look at this issue from a proof-theoretical perspective. We consider analytic calculi for certain nonmonotonic logis and analyze to what extent the presence of nonmonotonic rules can simplify the search for proofs. In particular, we show that there are classes of first-order formulae which have only extremely long “classical” proofs, i.e., proofs without applications of nonmonotonic rules, but there are short proofs using nonmonotonic inferences. Hence,despite the increase of complexity in the worst case, there are instances where nonmonotonic reasoning can be much simpler than classical (cut-free) reasoning.