Readings in nonmonotonic reasoning
An algorithm to compute circumscription
Artificial Intelligence
A generalization of collapsible cases of circumscription
Artificial Intelligence
A circumscriptive theorem prover
Artificial Intelligence
Compiling circumscriptive theories into logic programs
Proceedings of the 2nd international workshop on Non-monotonic reasoning
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Artificial Intelligence
General Domain Circumscription in its First-Order Reduction
FAPR '96 Proceedings of the International Conference on Formal and Applied Practical Reasoning
A simple formalization of actions using circumscription
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Efficient Reasoning Using the Local Closed-World Assumption
AIMSA '00 Proceedings of the 9th International Conference on Artificial Intelligence: Methodology, Systems, and Applications
Modeling Paraconsistent Reasoning by Classical Logic
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Second-Order Quantifier Elimination in Modal Contexts
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Proceedings of the 14th International conference on Industrial and engineering applications of artificial intelligence and expert systems: engineering of intelligent systems
A Second-Order Theorem Prover Applied to Circumscription
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Database Repairs and Analytic Tableaux
Annals of Mathematics and Artificial Intelligence
Reasoning with infinite stable models
Artificial Intelligence
Complexity of propositional nested circumscription and nested abnormality theories
ACM Transactions on Computational Logic (TOCL)
Loop formulas for circumscription
Artificial Intelligence
The PMA and Relativizing Minimal Change for Action Update
Fundamenta Informaticae
A Correspondence Framework between Three-Valued Logics and Similarity-Based Approximate Reasoning
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Reasoning under minimal upper bounds in propositional logic
Theoretical Computer Science
Improved Second-Order Quantifier Elimination in Modal Logic
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Literal Projection for First-Order Logic
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Loop formulas for circumscription
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
First-order Generalization of the MPMA Belief Update Operator
Fundamenta Informaticae
Learning partially observable deterministic action models
Journal of Artificial Intelligence Research
A new perspective on stable models
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Computing strongest necessary and weakest sufficient conditions of first-order formulas
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A temporal logic-based planning and execution monitoring framework for unmanned aircraft systems
Autonomous Agents and Multi-Agent Systems
Loop formulas for circumscription
Artificial Intelligence
On the correctness of rough-set based approximate reasoning
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Artificial Intelligence
Loop-separable programs and their first-order definability
Artificial Intelligence
Tractable model checking for fragments of higher-order coalition logic
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Probabilistic event calculus based on Markov logic networks
RuleML'11 Proceedings of the 5th international conference on Rule-based modeling and computing on the semantic web
Quantifier elimination in elementary set theory
RelMiCS'05 Proceedings of the 8th international conference on Relational Methods in Computer Science, Proceedings of the 3rd international conference on Applications of Kleene Algebra
On the fixpoint theory of equality and its applications
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Living with inconsistency and taming nonmonotonicity
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Projection and scope-determined circumscription
Journal of Symbolic Computation
Sahlqvist Correspondence for Modal mu-calculus
Studia Logica
First-order Generalization of the MPMA Belief Update Operator
Fundamenta Informaticae
A Correspondence Framework between Three-Valued Logics and Similarity-Based Approximate Reasoning
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
The PMA and Relativizing Minimal Change for Action Update
Fundamenta Informaticae
Meta-Queries on Deductive Databases
Fundamenta Informaticae
General Domain Circumscription and its Effective Reductions
Fundamenta Informaticae
A Reduction Result for Circumscribed Semi-Horn Formulas
Fundamenta Informaticae
Automated Generation of Logical Constraints on Approximation Spaces Using Quantifier Elimination
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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In recent years, a great deal of attention has been devoted to logics of common-sense reasoning. Among the candidates proposed, circumscription has been perceived as an elegant mathematical technique for modeling nonmonotonic reasoning, but difficult to apply in practice. The major reason for this is the second-order nature of circumscription axioms and the difficulty in finding proper substitutions of predicate expressions for predicate variables. One solution to this problem is to compile, where possible, second-order formulas into equivalent first-order formulas. Although some progress has been made using this approach, the results are not as strong as one might desire and they are isolated in nature. In this article, we provide a general method that can be used in an algorithmic manner to reduce certain circumscription axioms to first-order formulas. The algorithm takes as input an arbitrary second-order formula and either returns as output an equivalent first-order formula, or terminates with failure. The class of second-order formulas, and analogously the class of circumscriptive theories that can be reduced, provably subsumes those covered by existing results. We demonstrate the generality of the algorithm using circumscriptive theories with mixed quantifiers (some involving Skolemization), variable constants, nonseparated formulas, and formulas with n-ary predicate variables. In addition, we analyze the strength of the algorithm, compare it with existing approaches, and provide formal subsumption results.